Subscribe2 and Google Account

I have a client that has a Google Account, and email addresses are run through Google.

My question is this: Does that impact the email process with Subscribe2?

I know there have been numerous posts about this, but GoDaddy is the host for my client so I suspect the problem lies with them. Since the email is generated by the WordPress site, which is hosted on GoDaddy, the emails don’t make it to the gmail servers until they’re handled by GoDaddy?

Help.