the connectors are the same.
But the HD 6970 has a much bigger heatsink with 3 heat pipes(the 4850 and 5750 have only 2 heatpipes) and might not fit in a iMac 2010 model. It also means it produces more heat and has a higher tdp of 75 watts. I can't find the tdp of the 4850 but the mobility 5xxx series doesn't go higher then 50 watts so i expect that will be the same for the 4xxx series.
iMac's 2010 and 2011 use the same power supply's so the higher tdp might not be the problem.
I've heard Apple uses a custom firmware on its gpu models so 3'party graphic cards won't work.
This means the system checks what graphic card is installed and might also check what model number is installed and reject the different model. But this doesn't have to be the case
Maybe it only checks if a Apple firmware gpu is installed and it might work fine.
Just make sure you can return the HD6970 if it doesn't.
Good luck and let me know if you succeed.