Yes, they'll be able to do this with no problems. Last year we received a check with tax returns and it had both my and my husband's name on it. I had to sign the check and we deposited it to my husband's account with zero problems.
It depends on your bank and if there is an AND or OR between the names. If there is an OR, you can put under either account but it it is an AND between the names, you may be required by the bank to have both people present.