I don’t know what the experts say, but I suggest you reverse the process. Pre-emergent weed killer prevents all seeds from sprouting so your grass would not grow and you would have wasted your money.

A better choice might be to treat the area with either something with a short life that kills everything, like Roundup, or a broad leaf weed killer, which won’t affect grass, then broadcast the grass seed, wait until it is growing well, and then put down pre-emergent weed killer to keep any new (and presumably weed) seeds from sprouting.

In my experience in Texas, pre-emergent weed killers seem to last up to two years. At least, that is how it is in my yard.