Rocksmith is, I would say, more forgiving of timing issues than incorrect note issues. I’ve seen it pop up a little “LATE” on some notes/chords, but not as often as “MISSED.” Things like string muting and proper tension in your fretting hand (I went from a Strat to a PRS and was fretting chords out of tune due to gripping too tight).

It does feedback if you hit the wrong note (or it thinks that you hit one), but it doesn’t really outright tell you about your timing and will accept some horrendous timing if the note was right. In fact that is one of the major points people seem to mention as its’ drawbacks.
Although I would personally say that Rocksmith has been pretty pivotal to my timing (along with recording), since at least for me it multiplied the time I was playing to a rhythm of a background track. The game allows you to loop and slow portions of songs that you like and play the parts on repeat against the original song with a relatively nice and fast interface, way faster than doing it yourself on a DAW. And that little convenience has me playing to rhythm way more than I would otherwise at home by myself, and especially work on hard parts slowed down.

Rocksmith is really fun for playing songs with official backing tracks. As a learning tool, it’s really limited. I have both Rocksmith 2014 and Rocksmith+. 2014, IMO, is the better of the two. The ability to mod 2014 and add custom songs gives you the ability to increase the library WAY farther than the stock DLC.

If you really want to get into it (and this is where I started having the most fun), check out Tonelib-Jam. You can write or deconstruct songs (even using RS2014 files) using the editor that gives you both tab and standard notation, plus it’s got a “play along in 3D” mode that works just like Rocksmith does.

My go-to at this point for just cranking along with some songs is Tonelib-Jam plus whatever songs I feel like grabbing from customsforge.com