It's possible to get a rough idea. In fact, Dawkins book 'An Ancestors Tale' might have mentioned it. But it's years since I read it and I couldn't find my copy when it came up in discussion on another thread.
...what one could do is note (as he does in his book) the major changes that took place from us back to bacteria. If you took each of his stages, estimated how long they existed in their specific species before branching off into the next ancestor, you'd have a list of all previous ancestors (well, best guess at the major ones) and the length of time they existed. I did find a rough compilation that someone had done from the info in the book.
Monkeys and apes: 40MY(3M)
Mammals: 180MY(120M)
Reptiles: 310MY(170M)
Ray finned fish: 440MY(195M)
Sharks, hagfish and lampreys: 530MY(240M)
Lancelets and all chordates: 560MY(270M)
Multiply each length by the time it took any given species to reach maturity so you'd have the number of generations. Add them all up and you'd have a very rough idea of the number of generations between you and your earliest common ancestor. Someone here
Can we make a rough estimate of the number of generations since the origin of life? estimates it to be 1x10^12 generations.
How many generations does it need to produce a beneficial mutation? Well, now we have the same problem as the Drake equation for estimating the number of alien civilisations. You don't have exact figures with which to work. But you can plug in something that sounds reasonable and see what it gives you.
Bear in mind that there may be a few large mutations that give an evolutionary benefit or there may be very many that give small incremental benefits.
It's an interesting question but not one that's going to get you a very accurate answer.