There is a problem report that Gramps works with ChromeOS but with an unresolved problem with the Gtk interface library. A drag’n’drop incompatibility exists — it drags but won’t drop.
So that equates to a “No, Gramps is not fully compatible with Chromebooks.” Sorry.
Despite that drag’n’drop incompatibilty, @GeorgeWilmes reports that he has been using Gramps on a Chromebook for several years.