Maybe a few of the crazies will worship the Horned Rat, or pray to some unknown Rat Deity to protect them - perhaps ex-sewer patrolmen, as they seem the most susceptible.
However, for the majority of the Empire population, the Skaven threat, and the Under-Empire doesn't exist - they're blissfully ignorant concerning it. In the Breton and Kislev, they're more widespread, but both due to the nearness of the Chaos Wastes in the latter and the Forest of Arden in the former, they are likely to be assumed as different forms of Beastmen - which in a way they are, but aren't, in that they're mutated rats, rather than mutated humans. But for those reasons, its unlikely that more than a couple of isolated individuals or perhaps hamlet/cult, no sane person would worship the Horned Rat, doubly so if they actually knew of the creatures under his control, and especially as he doesn't especially have any real power giving properties.
However - the Vermin Lord is apparently a Daemon of the Horned Rat, "summoned from beyond the veil". It is mentioned as a Living Avatar of the Horned One, of whom even the council of thirteen fear.
He was actually summoned - himself - once during the Civil War. The summoning process is described to require blood sacrifice - although apparently quality is not an issue, and is more to do with the signifance of the numbers - similar to the ritualism of Chaos, although like Skaven, are typically less on the quality. So, 13 thirteens is the number of Grey Seers, and 13 thirteens is the number of sacrificed slaves.
By the looks of this, he could well be a particularly powerful Daemon, unaffiliated to one of the existing major powers; similar to how Be'lakor is. Maybe he came into power similar to how emotion brought the 4 Major Powers into being, or maybe the Skaven came into being by the daemons designs. I don't think much has been talked about the Horned Rat a whole lot much - as the Skaven power seems to come from Warpstone, rather than a divine presence.
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