Theoretically, yes.

The default setting, when you list an item, is to exclude all bidders who have "2 unpaid item strike(s) within 1 month(s)". This should mean that once the non-paying bidder has bought twice, and not paid, and has receiced 2 unpaid item strikes, they will be prevented from bidding on any default-setting listings until the one month period has elapsed.

Of course, that doesn't stop such a bidder from doing the same thing next month, so I personally have my setting to exclude those with "2 unpaid item strike(s) within 12 month(s)". You can adjust this when making your listings.