We're currently in the process of finding a flat in Nottingham. We'll move at the end of August, but we'll be in America from the last week of July well into late August, and it seems that the flat we had in mind might fall through--the agent is very reluctant to send us pictures of the flat; we've seen many flats for sale in the same building, and they all seem to be very similar. The agent has told us this place is comparable to those, but seems to be very computer illiterate and has now agreed to MAIL us a disk with pictures of the flat... oh boy.

We were in N'ham a week ago looking at flats, and this agent showed us another place, so we have actually met him. It seems as though we'll get the place if we want it, but as the pictures are taking so long we are starting to consider plan B's.
Now, we have two cats. For this place they're not a problem, but if it falls through we're going to have to look again. Many places have said they don't accept pets when we've asked.
1. What would be the repercussions of renting a flat that might not accept pets, if we don't ask and play the "dumb foreigners" card?
I realize it's dishonest (no lectures please), and it's not like we're planning on doing this, but just in case we run out of options.
2. As it's likely that there would be a "no pets" clause in the contract for a place that doesn't accept pets, what would happen if we moved in with the cats?
3. Do agencies run tenant checks (as in visits to the property), and if so, do they give advance warning?
This is a bit tricky because we're not living in the UK, we'll be away for three weeks (sucky timing but can't be helped), and we'll have a 2-week window to move ourselves, our cats and have our stuff shipped.