Not really in Aginor's case. I have a hard time believing that you can draw so much power you kill yourself without first burning out (or at least simultaneous death/burnout).

As for Lanfear's burnout/stilling then being healed. A couple of points.

1. Don't you think it would have wound up being mentioned by one of the FS women if she had to heal a saidar connection? We've had POVs from all the potential candidates and realistically Semirhage seems like the only one with the inherent Talent to pull off the Healing. Moghedien is noted to be ridiculously blind to areas of the Power which she had little ability or interest in, so your assumption that she would have picked up the weave in the rebel camp is thin. One of the Rebels is possible.

2. Taking Siuan and Leane as examples Cyndane would be so weakend by being healed by a woman that she wouldn't be anywhere close to Forsaken strength, much less stronger than Graendal or able to fend off Alivia with *angreal (Siuan lost 2/3 of her strength) ... if you assume a 100pt scale, Cyndane would have dropped down from 100 to 33, making her more like a regular AS (ish).

3. Cyndane specifically points out the connection to her lowered power and her time spent with the 'Finns. Seems like a big hint in there somewhere.

Anyway, while I don't think your theory is impossible, I also don't know that I would call it the most simple explanation!