I have used loads of USB mice and keyboards and those little adaptors always work with them.
(apart from situations where the little adaptor was picky and the computer's usb port was picky. I had a bunch of little adaptors, different makes. The good ones worked always. No special circuitry. The USB mouse/keyboard always supported PS2.
The issue is the other way, Ps2 to USB, then you need a big adaptor with special circuitry.
By the way, when I tried USB-Ps2 adaptors, some slightly larger green ones that looked like the ones you pictured, were a bit picky, but some slightly smaller ones that happened to be red and purple seemed more reliable in that they seemed to work in all my computers including a picky one(they were from a convenient rip off elecronics store called maplin).
I had also heard that all USB mice/keyboard seem to support Ps2. My experience of them is that.. I have tried many USB mice/keyboard , cheap ones, and without me having to check, and they've all supported them. Though I suppose it's possible maybe there are some that don't and you could get unlucky, but I doubt it!
The mouse is cheap and finding out if it works is like less than a minute once you get the items i'd just buy it and try it.
I don't know about losing dpi. I just use mouse/keyboard like a normal joe and don't know about dpi in regard to mice.
Ruslan (in 2019) comments "I've also used lots of USB mice, and until now I hadn't come across one without support for PS/2 via an adaptor. But now here it is: I replaced Logitech M-BJ58 with M100, and... it doesn't work in PS/2 port, although it works fine when plugged in directly into a USB port, and M-BJ58 does work in both. Dunno how Logitech could throw away such a trivial piece of functionality, but it's so. ..[and am] not alone with this combination of the replaced and replacement mice, see https://community.logitech.com/s/question/0D53100005101CqCAI/how-to-get-m100-mouse-on-ps2-port
It might be that as we move forward (in time), some other new USB mice might not support ps2! (as ps2 is more and more phased out)