My OPINION (you know what is said about that???), I'd say NO unless it states the course covered everything in DE code 1441 a-j. If it is a NRA Basic Pistol Cert, I'd say no.
If you wanted to try it....
Run your ad NOW
Get your references NOW
Schedule finger printing (FP)
Ad must be run ONCE in a news paper with (I think) 35% circulation in your area. Must wait 10 days after ad to file. If you schedule for finger printing now (Troop 2) I think it will be 2-3 weeks before they will get you in. If you go to Dover, walk-ins welcome. Once you are FP'ed, you have 30 days to file. If you take more than 30 days, you have to be FP'ed again. Then you wait.. and wait.... and ....
If all goes well, you'll get the DOJ letter. Then a week to 2 weeks later you will get a letter from the court. Stating you have 90 days from the date of the letter to turn in a cert or the application will automatically be denied.
I did my training AFTER receiving the 2 letters.
If you try this, I'd make SURE I could get the training BEFORE the 90 days are up.
Oh, BTW, the waiting SUCKS!