You know, conventional wisdom says no, but I have found it to be a big annoying maybe. I have very soft synthetic flats that stretched, but stiffer synthetics probably won't. I doubt you can take it to a cobbler and ask for it to be stretched, as most cobblers are pretty old school and don't want to risk ruining the shoes and getting in trouble.
I'm interested in trying this brand which claims that its materials are 100% vegan and stretch and breathe just like real leather. If so I fail to see the need for real leather...but we'll see.