My school had my documents messed up, and I was forced to stay a bit longer. Unfortunately I found out too late to get an extension and I am on a one day overstay. Is it possible to get a 7-day extension , pay the one-day overstay fee, and leave in a few days?

Yes you can.

Again solid advice from Ubonjoe. I was out one day for my Non O extension but went to Bangkok, got the Stat dec from Aust embassy and got back to Jomtiem just in time and paid the 500 and went across the floor and got the extension done.

They wanted to see the overstay fine payment receipt before issue of the extension. Of course where you do it may have a different sequence.

 

My situation was a bit different. I wasn't trying to stay in Thailand. I was in Thailand for holiday. Planned on staying 30 days. At about the 25 day mark I realized the company that bought my tickets for me had me flying on the 31st day. I went to the Immigration Office to ask about an extension. The Foreigner at the Information Desk at the entrance said I didn't need an extension if I was leaving on that day and I wouldn't have to pay a fine. When I went through Immigration I had to go to a desk behind the Immigration Counters. The Officer wasn't happy but She gave me another stamp said you're bad don't do it again and then let me go. No fine. 

4 hours ago, firemans35 said:

My situation was a bit different. I wasn't trying to stay in Thailand. I was in Thailand for holiday. Planned on staying 30 days. At about the 25 day mark I realized the company that bought my tickets for me had me flying on the 31st day. I went to the Immigration Office to ask about an extension. The Foreigner at the Information Desk at the entrance said I didn't need an extension if I was leaving on that day and I wouldn't have to pay a fine. When I went through Immigration I had to go to a desk behind the Immigration Counters. The Officer wasn't happy but She gave me another stamp said you're bad don't do it again and then let me go. No fine. 

The fine for just 1 day overstay is waived at Bangkok airports, but is recorded.