for the most part, your idea isn't against the fluff in anyway. lets break it down:
Basically, the army is a "chapter" of Space Marines
GW use the term 'chapter' in three different ways:
1) a specific form of subdivision of a Space Marine Legion.
2) a specific organisation as defined by the Codex Astartes, displaying key attributes, including having a single geneseed and founding, following the tactical advice of the C:A and having a high percentage of Officers, but specifically NCOs. this form of Chapter is modelled on the previous.
3) a honorific epithet given to Imperial SM organisations that do not follow either of the two above definitions and are thus not chapters in any real sense. this is largely due to the fact that Imperial law states that all Marines must be part of a Chapter as defined by the C:A, but this is difficult to police and not a very political intelligent move to police it too far anyway. thus the term is often used in the phrase 'non-codex Chapter', in an attempt to differentiate between real chapters and other forms of organisation.
all three definitions are quite specific and provide certain limitations to what can and can't be true of them. from the sounds of it, you are suggesting a group as defined by 2, that has become a group as defined by 3 (or not
defined as might be more appropriate).
the problem is that 3's are not made from 2's.
that would imply that the chapter has been founded and then rebelled against Imperial law, which, by anyone's standard, is enough to get you put on the blacklist. the only way a 3 would come into being is if it was specifically created that way, with the aknowledgement of the Imperial government (if not their permission).
who view the Codex Astartes as too limiting, and seek a more open minded (some might say, radical) approach to dealing with the enemies of the Imperium.
lets not forget that the Codex: Astartes was written by a Space Marine for Space Marines. it was deliberately designed to be easily accessable by all marines and be helpful in all situations. the majority of ojbections to it stem from the fact that it ties marines to a system that prevents them from opperating in the personality cults that the Legions had grown used to. chapters have less personality and are more closely monitored than Legions were. hence several Legions chose to simply ignore the demands of the C:A, and a number of Chapters since have been soggy with nostaglia for the 'old days'.
i can't think of any 'official' Chapters that have rejected the dictats of the C:A after there creation (save those from the 2nd Founding, who are of course the same marines as the 1st Founding).
Thus, this "chapter" has alligned itself with an Inquisitor who shares their view that the only way to truely defeat the enemies of the Imperium is to turn their own weapons against them (a Radical). Now, this Inquisitor, while a Radical, is an Oblationist, believing that the the daemon, the psyker, and the xeno are evil, but recognizing that some must sacrifice themselves in using these evil means to protect the Imperium.
to be entirely honest, that is fairly standard fair. its not hugely imaginative or clever, and its a little irksome to imagine that the Inquisition and Astartes are really all that close or willing to be allies, but if its what you're going for then there's no real issue.
Now, that being said, here's my question. Would it be fluffy for the Space Marines that make up this chapter to come from a mix of existing chapters?
not if you are still imagining them to be the 2nd kind of Chapter. that is a club that is tied together by genetics and is near impossible to leave. even CSM don't much like switching between chapters (Fabius Bile and Ahriman haven't had much to do with their Legions since the Heresy, yet are still very much a part of them). Chapters (and Legions for that matter) are familial groups and one can't simply abandon them, just because they are no longer in favour. in fact as you rightly point out, if you were to attempt to change your 'Chapter' you will likely recieve a death sentence.
however, it's perfectly possible for someone to be other part of a Chapter and of a non-standard SM organisation, similar to the Death Watch (though with a different purpose), and still be regarded as loyal.
Can Space Marines who drastically disagree with the Codex Astartes leave their chapter without the penalty of death?
one would have thought not. in fact drastically disagreeing with the tome might land you in hot water unless you of the most venerable nature.
While I'm sure some chapters would support doing this, and might very well see seconding or permanently assigning some of their Marines to this chapter as a high honor, I could see some more traditional chapters being utterly opposed to the idea, going so far as to execute any who abandon their chapter.
i can't personally see why it would ever be supported or even considered an honour. SM Chapters are highly insular and if nothing else could not afford the loss of geneseed (as they are not able to replicate it themselves).
what strikes me as more likely (and a more interesting story to boot), is if you chapter was a front for another, altogether more subversive organisation. to illustrate; imagine the Doom Strikers chapter, who have become increasingly disappointed by the restrictions placed on them by beligerant imperial commanders who are all too human, and use the C:A as a way of trapping them. after a particularly successful campaign, which they led, they formed a brotherhood of sorts, which only the most deserving members (of any chapter) were invited into. this would be seen as an honor and in no way threatening to the security of the recruited Chapters. however, the brotherhood is simply a secret society for those disatisfied with the current system of human oppression. they work together openly as a team, but their goals are hidden from everyone but the most astute.