Potential risks of users connecting to SQL Server, through Excel, as sysadmin?
Pretty much everything. 

I'd start with their potential ability to use xp_cmdshell (and sp_configure if they can't, so then they can ... and whatever the account returned by xp_cmdshell 'whoami.exe' can do....), then move onto their ability to do drop database.

Further risks include not just finance users being able to do these things, but any program on a finance machine gaining access to your sysadmin connection credentials...

(Other potential risks include the risk of discovering that one of TPTB set it up this way)