The only problem with cutting T-shirts and other knits before putting on stablizer is that they tend to curl along the raw cut edges which makes applying the stablizer go less quickly when you are finally ready. I am one of the few who cuts first and then do my iron on stablizer, but I do it right away, cut my square then immediately iron on my stabilizer which has also been cut to the same size as my square. I do get a bit of distortion sometimes but not often and have always been able to use the block with no issues.
A great alternative is to starch the dickens out of them. I would get some sta-flo starch, can usually find it in large jugs in the laundry section of Walmart. Make it fairly strong, like half and half and make it in a bucket or something large enough to simply dunk them. Dip your knits into your starch, wring them out well and hang them on the clothes line to dry. Don't worry if they are a bit wrinkled you can press that out later. Once dry you can "butcher them down" to an oversized cut of what you want to save from the T (usually the logo or imprint). Then, not only can you cut and store them, you may just be able to sew with them without stabilizing. I have heard of people doing this to avoid doing stabilizer but I have never been brave enough to try.