That's a good idea and works better than just asking "if" they will reimburse.
Yup for sure, if it's just put across in a matter of fact way - basic admin query etc. acting like it's standard (I mean really it is rather standard) then I think there's much less potential for drama.
I'm just concerned that the information passed onto to me via agent stated that I would be informed of "the hotels others will be staying at" which implies that I'll have to sort out and pay for my own.
Maybe, but I'm not so sure - the mention of hotels others are staying at could also be because those are the ones they're willing to pay for (and it's also just a nice thing for you to be staying at the same place). It would still be fairly normal for you to book your own and expense it back to them rather than them to pay for you directly as they might for some staff members.
