I know I have seen this asked before and I have been curious about it myself, so I did a test purchase of a gc on the Kroger website...
I did earn the 4x points on my variable ebay virtual gc (with the 4x digital coupon). I did not earn additional cb from my BCP for a supermarket purchase... it was processed as "Merchandise & Supplies". Side note - it took about 4.5hrs for delivery, so plan ahead if you are trying to top up for the month. Points don't post til the order is shipped/emailed.
I've added this info to the wiki in case anybody else has questions about it in the future.