I'd like to use git submodules to track subprojects. I'd also like to have the subprojects' code directly contained in the parent repo, for convenience. Is it possible to inline a submodule such that the parent repo contains a snapshot of the child repo's content at the submodule's commit?
Not with submodules. Submodules are always separate repositories.
Try git subtree. It allows exactly that — to inline a repository inside another. Then you can decide if want to push changed files back to the source repository.