I would hire a vocal teacher and ask them this. If you're asking if Logic can make you a great singer- no it can't. If you're asking if Logic has powerful editing tools that can clean up a solid vocal performance- yes it does. But the only real thing that can help your singing IMO is practice, breathing, and other traditional techniques that a good vocal teacher could probably help you with.
If you can intonate and can adjust yourself onto pitch on your own, you can learn the rest. You don't need absolute hearing but you do need relative hearing, notes in relation to a key-note. Practice can take away wobbliness which is muscle-tension but the mind has to be able to intonate. Can you whistle a song correctly? Then you can intonate.
You can also work on your singing style.
If there's a particular note, or passage, that you can't get to sound quite right with "proper" singing - Try speaking, shouting, whispering, etc it. There are lots of songs that sounds great even though the singer can't hit or hold a single note.
I cheat like this all the time - Or I use backup vocals by someone who can sing, or fill out (or replace entirely) with instrument on crescendoes and such.
Any particular plug in settings which help most? I've tried pitch bender, and adding reverb/chorus but clearly if you're not quite in tune it just sounds worse. I am pretty musical and can sing ok, just realistic that I'm not a great singer. I want to add vocals to my tracks to attract a collaboration with a good singer, but am concerned my vocals as a guide vocal just take the track from being pretty good musically to sounding quite poor!
It sounds as if what you're really concerned with is the character of your own voice, more than the actual singing quality.
You can try to tone that down a bit with things like compressors and/or eq. If you're lucky, tweaking it slightly with something like the formant setting in the vocal transformer can help. Once you've been able to take the edge of whatever bugs you most in your singing, you can probably start adding chorus, reverb, etc since they'll no longer just augment the "bad" sounds.
If you do this regularly, you really should invest in the melodyne plug-in. It does just what you ask for, it places notes on pitch and also takes care of the pitch-drift that often accurs. Once you know for sure that your notes will be on pitch-center, you will actually start to sing better and more confident.