Does it make sense to have a Back button on Step 2 of this particular wizard?

Step 1 of this wizard must be a Sign Up form. In Step 2 and the rest of the steps, we list down some questions to ask the user.

In Step 2, does it make sense to have a Back button?

My thinking is that in wizards, we should always offer a way for users to be able to go back to the previous step, but does that make sense in Step 2 in this particular scenario where Step 1 only contains a username/password?

One option is to start the first step after the signup form, but that may be a deterrent to some people (ie having to signup first before they can do anything else). However, if we label the signup form as the first step, they may see that there are only 4 remaining steps so it may be less of a deterrent (ie it only takes 5 steps so I may be more inclined to sign up)?