I say yes, if asked. Sometimes they may write liquid on the box, often they do nothing. I also put "perishable" stickers on all my boxes. This is because if you are shipping express and it takes more than 3 days, you can file an insurance claim to recoup your losses (beyond the shipping costs) even though they dont cover live things. If its clearly marked perishable and it is way over time, they will cover it just because of that. Plus, its honest.
I do not mark live. This is because USPS changed their rules about a year ago that if something is marked live, it gets put on a special part of hte plane to control the atmospheric pressure (relavent for live things like birds, etc, not so much for fish) and that shipping can be delayed in order to do this.
Also, with UPS, they don't have temp controlled vehicles so I try not to use them unless a neighboring zone. FedEx has destroyed every single box I have EVER sent using them.
I shipped probably 4000 boxes so far this year using USPS. I have had issues with 6 using USPS. Those 6 sucked, but with fedex out of 12, 12 issues. With UPS out of 30 or so, 5 issues. I am sticking with USPS.