When I bought my new machine (P4 1.3Ghz, 128Mb RAM, WinME) I ran my Hong Kong copy of SF4.5 with no problems. Since then I bought SF5.0 and Vegas Audio and both run with no problems whatsoever. I would recommend a clean install of WinME (meaning on a freshly formatted HD; don't upgrade from Win98SE to WinME).
Of the utmost importance here is making sure that ALL of your drivers are up to date. If you have the very latest drivers you should have no problem using any audio software on WinME.
Also very important is the speed of your machine. People who install WinME on an older system with a slower Front Side Bus and HDs that don't support ATA mode 5 (which is currently the fastest mode that supports 100MBps transfers) are asking for some heartache. Keep in mind that WinME requires far more TSR programs to start up. These can be killed one at a time by pressing CTRL-ALT-DEL and closing everything but Explorer and SysTray.
Provided that you have the latest drivers and a bit more than just the "minimum system requirements" for WinME, you should have a trouble-free experience with WinME. But as is sometimes the case with Microsoft, things just don't work no matter what you have.
It's really a crapshoot if you're upgrading from Win98SE. I'd stick with what you've got already. When you decide to switch to a new machine that comes loaded with WinME, you'll have a far better chance of success using your audio programs on the new computer.
Hope this helped.
Dr3