I do use neem on my indoor potted herbs with pretty good results. Have used with both fungus gnats and whiteflies. The problem with the neem & fungus gnats is that it doesn't treat the soil where they breed, so it is only so so effective. I use in combination with sticky traps, and it's kind of an "it keeps under control but doesn't eliminate". I have not had issues with seedlings, so cannot specifically address, but think you should be fine if you start light.

Here is a link that might be useful: Pot plant sticky traps