Sure you do that. I wouldn't recommend it though, but yes you can. This is essentially just a mycelium innoculation instead of multi-spore germination. However you cannot sterilize the mycelium as trying to do so would almost definantly result in the destruction of the mycelium.There are a couple of better methods that I would use in place of this however. Check it.
1. Don't wait for your substrate to fruit. Once it is 100% colonized then you can be pretty sure that the mycelium is virile and thriving. Let's say you have 11 out of 12 1/2pt jars that survived (we'll subtract one due to possible contamination). I would use the other 10 jars exactly as you were planning on (birthing/casing) and reserve one jar. Keep this jar in a cool environment until needed, this is now called a "Spawn Master" (I wouldn't store it longer than a week to ensure 100% effectiveness, although in theory you should be able to store them for months under proper conditions). Now after you have birthed/cased the other 10 jars and thoroughly cleaned the contaminated one, sterilize them and prepare another batch the exact way. Except this time don't use spores. Use substrate from your "Spawn Master". Use about 1/10th of the Master per jar. Place them in the incubator and wait. You should notice growth in a couple of days. Once these jars are 100%, repeat, saving one jar and starting again.
2. If you are already too late in the game for this to be a viable option, don't fret man, we gots ya covered :P So you've already cased/birthed all of that beautiful mycelium? No problem, once you have mature fruits prepare another batch of jars, take a nice big/healthy looking shroom, and in a sterile environment and using sterile tools slice open the stem of the mushroom lengthwise (one big long cut up and down the middle of the stem). Now using a sterilized scalpel/knife cut a small chunk of shroom out and place it in your jar, repeat for the rest of your jars. Put them in incubatin' conditions and wait! When they are colonized, I would use step 1. as it's a bit simpler.
If you do this you can successfully shed about a week from your total production times. Doing this essentially bypasses spore germination and established a healthy myclial "core" fast, and that helps to beat out would-be contaminators.
Hope this answers your question and helps!