So my other guitar player needs to be heard and all we have lying around is a Fender Rumble 30 bass amp.
What would it be like if we ran a strat into it? What about if we added some pedals in front as well? Any adverse effects on the amp?
It probably won't sound as good, but start with the volume low and slowly increase it until you reach your desired volume. Stop if it sounds like the speaker's having difficulty keeping up when it start to flub and spurt and fart out.

The amp will be fine, but bass speakers aren't always designed to handle the higher frequencies of a guitar. That said, it usually won't always destroy the speaker, but it won't always sound good.
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It'll sound like shit, but it's a Fender Rumble, they're built that way. Shouldn't do any harm.