Currently on a road bike with a 9-speed Sora groupset, I have a spare 10 speed Shimano 105 chain, will it be compatible with the sora ?

Not an expert but I don't think so. 10 and 11 speed chains are narrower then 8 and 9 speeds.

Yes it will work with index shifting. Friction shifting can cause some minor performance issues for the FD (I friction shift my touring bike) . I'm presently using a friction shifted 9 speed setup on my touring bike. But for awhile, the bike drivetrain comprised of a 9 speed trekking crankset and a 10 speed cassette. When shifting the FD from the big to middle ring you could actually get in a position where the chain was actually floating between rings but the gap was not wide enough for the chain to get stuck between rings. My setup is now completely 9 speed including the wider 9 speed chain and that is no longer an issue.

As mentioned before, you probably won't notice a difference if index shifting. Al

That's correct about chain width but, yes, a 10-speed chain will work on a 9-speed drivetrain.