Yes, they count. Late payments are late payments and they have the same impact on your score on an open account or a closed account. They'll be there for 7 years. The 30's and 60's from what I understand will only impact your score for about 2 years, where the 90+ ones will impact your score for much longer.
Unless the lates are removed, the only thing that will ease the sting of them is time. What matters in terms of scoring is how long ago the late occurred, not whether or not the account is open or closed. In fact, if you closed an account 3 months ago and 4 months ago your second to late payment was late on that account, it will carry more impact than a late payment 2 years ago (but none since) on a current, open account. It's all about what was more recent. Hopefully that makes sense.
I've had GW success with current/open accounts but have not had any success with old/closed (paid in full) accounts. I suppose the theory here is that they have less incentive to grant you GW if the account is closed as you aren't still making payments. What I would suggest doing and what I do is lead them to believe that you want to open another line of credit with them, whether that is true or not. Like say it's a Care Credit card or a Lowe's card (both Synchrony Bank) in your GW letter explain that you have a bunch of dental work you need to get done or you have a kitchen remodel that you want to do and are thinking about applying for additional credit but you're apprehensive about doing so because even though your past account is paid in full, you have those late payments showing. This then provides the creditor with at least a little incentive to grant you the GW as they see the incentive being that you could again become their customer.
