If they shut down public data access, you can bet the programs will be shut down soon after.
And before you counter that there is a difference between data/research papers and "real" things like tanks, the government (and the media industry, and the scientific industry, and...) don't see it that way. It is intellectual property, owned by the US government.
Of course this doesn't mean people can just hack into the EPA servers, so to speak, but I would imagine it will not be very long before the administration is deluged in FOIA requests and is forced into making difficult choices about which information they will attempt to withhold from public scrutiny. If past experience is anything to go by, Congress will attempt to slow that process by continuing to underfund the judicial branch, but once the suits start to pile up you'll begin hearing the phrase 'writ of mandamus' a lot.
Edit: I left out the italicized bit about the government in the original which may have confused some readers. Sorry.
Check out Government Accountability Office reports.