Yes you can. Just remember that if you change your password for your FamilySearch Account it does not automatically change your Church account password (and visa versa) as they are no longer connected.
@swlongenecker You can.. but if you use your Church account you will have to enter a verification code every-time. What I found works is you use the same email for Family search.. but change your password. I sorta kept the same. but changed a couple numbers. Then you can just sign in without a log in code.
I hope that helps you.
FYI, I don't think a verification code comes in to play unless you have two-step verification checked. But one other advantage to signing in with a FamilySearch Account over using your Church account is that with the FamilySearch account you can use the check box to stay logged in for two weeks at a time. Just hit sign-in or Tree and you will be in. But if you use your Church login you need to sign-in every day. You can use the same user name and password for both accounts if you want.
@Chas Howell this is a nice advantage to having both login's