"Are $2 bills appreciated for tips?"
A. If its the choice between a single $1 bill and a single $2 bill, the $2 bills are very much appreciated without a doubt.
B. If its the choice between a pair of $1 bills and a single $2 bill, some staff could not care less (money is money and each is worth exactly the same) while other staff will very much prefer the two singles because maybe they personally had or have heard of issues with others accepting the $2 bills.
Either way, you'll never hear any staff complain when presented a $2 bill. Now, if you start handing out $3 bills, their attitude may change.