If the Google account itself gets suspended, then all the Google services (including Google Ads) in that Google account, would also get into suspension mode.
Do you see something like "Your Google account is disabled", when you try to log in to Google ? If this is the case, you will also see an option there to Appeal. Click on that and submit an appeal. In that appeal option, you will have to provide an alternative email to which Google will email you their reply (and that decision is taken by their algorithms).
About "Will the ads keep running?". Ideally, if a Google acccount itself is suspended (disabled), then all the Google services (including Google Ads) in that Google account, would also get into suspension mode, this means that the ads in Google Ads would also stop running.
Make a note of the date on which your Google account got suspended. If incase the reply to your appeal comes as negative (we cannot restore your account, it is permanently suspended) AND you then do see Google charges on your payment method pertaining to AFTER the day that your Google account got suspended, then go ahead and dispute those charges with your card issuer / bank, because if a Google account itself is permanently suspended, then there is no way to contact Google again (pertaning to that particular Google account).