Small point,our tech manual quotes that the AFDS gets its V2 speed from the MCP window (ie not the FMC). Seems sensible to me as you can depart with the FMC inop....
Errrrrrm. Many moons ago when I was new to this FMC thingy (-200 lad) we took off without any perf data in the FMC. We had an aircraft with an aspirated TAT probe so the FMC came up with a full power take off based on that temp. Our speed bugs were set correctly so the takeoff and flight directors were normal (well a little excess thrust thats all-V2 was set in the window!). No drama!
On another line, we regularly do improved V2 takeoffs, with the improved V2 up to 25kt greater than the normal V2. So, wihilst in the sim, I had a go at an engine failure at V2 and V2+15 (ie. in the second case, normal V2+40!). We then worked out the climb gradient and the V2+40 case exceeded the V2+25 case. Keeping V2+15 IS going to help you!