John, it's worked for me for years, having buckets out partially filled with water that mice and voles jump into all the time. I've found them in empty buckets, but more often in buckets with water, so I assume they are looking for water. I also have a couple of garbage cans full of water for a quick bucket filling, and I even found one in there. Not sure how it even got up that high. I keep the lid on upside down so the tree frogs will stay in it and eat mosquito larvae. It happens at night, when there is all the running around. This past summer there were 6 in one bucket.
It doesn't happen every day, but every few days in my 8 buckets there is usually one. The only caution I would add is that a bird, that come in with the big flocks, to my garden morning and evening, will sometimes jump in the buckets, too. I hate when that happens, so I don't fill them up too much so it can get out again.
Don't fall for the My-Place-Is-Special, It-Won't-Happen-Here Syndrome.
Out here I'm always trying to find ways of not doing the standard issue human thing (eating the planet, thinking of other species as disposable and unimportant, destroying everything in my path, etc), and it's not easy to find a balance between my interests and those of the various creatures who want to make a home on my space. This seems to be working out reasonably well. I'm lucky in that they have stopped invading my yurt (probably helps that I have a put Borax all along the circumference of it on the inside...doesn't kill them, but it's really irritating and they seem to learn from the experience).