Yes, it can be done.
Extreme caution must be used when swapping the BIOS IC as it is VERY easy to damage ANY IC when you hot swap it.
Check out the BIOS recovery guide posted at:
http://www.amptron.com/
Click on support and then Technical information and scroll down to the BIOS recovery guide.
As to the second part of your question, there are a number of IF then Else issues with using a different motherboard.
1. The BIOS IC MUST be the same identical flash ROM.
Peal the label off of the IC and check the part numbers on the IC itself.
2. The core BIOS code MUST be the same make and revision.
Such as Award 6.01
A better option would be to use a flash ROM programmer. Jamco or 1 of the other electronics parts houses should have 1 for sale.
Then, all you need is to identify the flash ROM and set up the software for it.
Or, play it safe and use a 3rd party BIOS seller such as:
http://www.biosworld.com/
They sell programmed BIOS ICs for $24 US.
Chas