Yes, there is a letter issued when you make the appointment, I was asked about this lack of visa for a one way flight once and explained then showed them a print out of the visa insertion appointment at the airport and they accepted that. This was only in Phnom Penh though.
What will you do if they take another 10 weeks to complete processing your application?
If you still come to Thailand as planned then you need to consider your options, you can make an appointment to go and have the visa inserted at Chaeng Wattana immigration office using the concierge service which I think is now the only way they will do it (free on first usage) - I've done this a couple of times before and it's a quick process. They will phone you and locate you at the entrance prior to going directly to the desk that issues the visa.
The last time I did this I stood right in the middle of the almost empty large clearing on the ground floor of Chaeng Wattana and started waving when the phone call came in looking for me just prior to the appointment time, the woman from TE saw me immediately.
Of course this might not be so convenient if you're up staying way in Chiang Rai or somewhere else far away from the place they insist you report to for the visa insertion.
I would also consider the possibility that it may take longer to get the membership approved and subsequent visa insertion appointment than your permission to stay duration, especially if you're forced to enter on a visa waiver.