pre-approval for credit card?

In most cases yes. Unless they find out you have debt charged off from a prior creditor. Some banks may open your account with a limited credit amount and slowly build your credit limit as you show that you can manage your credit well.

This is an excellent way to build credit if you do not already have a card.

When companies send out pre-approvals they don't dig very deep into credit reports, so there's no actual guarantee that you would get the card, I started getting pre-approvals the day after I turned 18 (this was back before the market crash when they were still handing out cc's left and right and you could still get a traditional unsecured card at 18 with no problem even with no credit history).

But seeing as you have a checking account with the bank, then I'd say there's a good chance you'd get the card.

Nope

Means you passed their "pre screening criteria" to just get the mailing.

Doesn't guarantee you will be approved when they do a hard inquiry on your credit.