The only botched procedures actually mentioned in the game are resulting in a permanent coma.
Plus, let's look at NV:
- you have operated as a courier for a longer time than you have an amnesia (see, Lonesome Road)
- you're WAY too far from the institute to explain that as a courier being disappeared and replaced by a courser
So, prima facie, whether you're a courser or not, your amnesia had noting to do with that. It's just not evidence, since it's too late to be connected in any way.
- synth components are pretty obvious in both Fallout 3 and 4
- especially a courser "chip" is a rather bulky and hard to mistake piece of equipment
- they're also said to be quite obvious to non-trained people in, for example, the Broken Mask incident. Valentine says no less than that the BM synth was full of servos and sprockets
- Doc Mitchell operated on your brain and didn't seem to notice anything special
- in OWB they outright extract your brain out, and the only thing out of place is the bullet scar. That's explicitly mentioned as THE reason why the auto-doc had to correct its procedure
While I suppose one or the other might have missed your having a big glass thing and wires in your head, it seems very unlikely that BOTH would completely miss that.