Yes Avid can work the way you want. Probably.
With ‘loosey goosey’ TOD timecode then auto sequence is probably your friend, but copy & paste is not so hot in Avid.
With your 2 x camera sequences, find the one that starts first.
Add a video track and 2(?) audio tracks with Ctl&y and Ctl&u
Drag other sequence to source monitor and patch video and audio tracks. (Nb auto patch is your friend here)
Overwrite
You now have C2, say, on V2 obscuring C1 on V1
Apply a PIP (picture in picture) effect to the first clip on V2 and resize and repo to taste. Drag effect icon from PiP editor to a bin to save that effect.
Select all clips right on V2 (this is the time to assign the three ‘select’ buttons to a keyboard shortcut AND add the alt key so it doesn’t select filler)
Double click the effect you saved to bin and it will apply to all the selected clips
Now you can see V2 over V1. Hopefully you made the pip big enough that you can now sync.
Sync by moving all the selected clips right by the required amount (there’s a number of ways of doing this but hopefully you were close to begin with and then managed to slide with the nudge left/right shortcuts
If you got this far then edit as per FCP7, otherwise employ a trainer to work through it with you
Now Avid is a complicated beast but is a very powerful editor that takes time to learn well. Yes some of it is long in the tooth and it is less than intuitive. But think yourself lucky they haven’t decided to implement a linear edit system.