I can’t speak for the 2G version, but the new Nokia 3310 3G does appear to support some J2ME apps. I was able to install the last release of the Google Maps app, a weather app, and an email app that actually appears on the Opera Mini store. Some jads do say they’re not supported (Note Plus 4) and one had the character sets all messed up (Anyview EBook reader).
EDIT: I confirmed that I was able to side load an (untrusted) app I developed (a very long time ago) using Java 2 Micro Edition SDK.