Sure it would. About as useful as a first gen i5 motherboard is today. In 5 years, ebay will be flooded with Xeon E3-12xx V3 chips for dirt cheap and they should work in a H97 board.
The MSI H81I (like most 8 series boards)
supports every Haswell Refresh chip as long as you have an updated BIOS. Since you have a pre-existing CPU in an upgrade situation, flashing the BIOS is not an issue.
The reason to go with a 9 series board is that you have guaranteed support for Haswell Refresh chips out of the box. The G3258 is indeed a Hasewell Refresh chip, so a 9 series board is worthwhile on those merits.
Since this is a "mom PC", the H81I would be perfectly fine if you had another Haswell CPU that you could use to flash the BIOS beforehand.