Will the Shimano HG41 match nicely with a Shimano Claris derailleur? I am almost buying a bike equipped with a Shimano Claris group, and I am particularly fond of big hills. So I found lying around my place a new cassette HG41, 11-34 teeth, which is allegedly for MTB. Will the big cog adapt ok with the short road derraileur? Both are 8 speed.

I know Shimano has some compatibility charts around, but I couldn't really figure it out by myself. Maybe something related to too much caffeine right now.
In short: Yes.

I bought said bike, and tried the new cassete. It works on both big and small front rings, but the derailleur arm gets very very stretched on the big one. My opinion on this is that the 32 teeth maximum limit has a bit of a safety margin, so if in the next 100 km something bad happens, I'll update the answer. Otherwise, problem solved.

And I will try to avoid using that low gear, unless necessary.

Also, here is the resulting derailleur position on the worst possible scenario, which I avoid: