Yes, you get the upgraded luggage allowance. It likely won't show up in the app, but the upgrade conditions are very explicit on this, so you shouldn't have any problems convincing the checkin agent, or worst case claiming it back afterwards.

It's not clear if you get business standard or business light allowance if you are on a light ticket, but from experience doing this intra EU I had no issue checking three bags (two for business + free FB bag) on an upgraded economy light ticket. Ended up being a lot cheaper than buying two extra bags on day of departure (and as a bonus got 32 kilos per bag instead of 23).