The tables in
The Parker Story show 30 VH-/VHE-Grade 20-gauges made with 24-inch barrels, and 38 28-gauges made with 24-inch barrels. There were two 12-gauges and one 20-gauge made with 23-inch barrels. There are a couple of 28-gauges listed with 20-inch barrels. All this to say it is possible.
A check on the "Research Letters" serial number check on our home page shows there are surviving records for 156670. A Research Letter could answer a lot of questions on a potentially very valuable gun.
Wow!!! Why isn't something like that in my attic? My very first thought is that looks like late Remington era wood. A Parker Bros. VH-Grade in the 156xxx range would normally have wood like this --