No: the arrows are not magical
The Sage Advice Compendium provides clear criteria when something counts as magical:, namely if you can answer yes to one of these questions:
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
- Is it a spell attack?
- Is it fueled by the use of spell slots?
- Does its description say it’s magical?
In the case of the magical bow, which is a magic weapon, the description for magic weapons (provided in an erratum, p. 140 DMG) explicitly states the arrows count as magical:
If a magic weapon has the ammunition property, ammunition fired from it is considered magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
fullfillingfulfilling the last of these conditions. The bracers of archery are not a magic weapon, they are a wondrous item (p. 156 DMG):
BRACERS OF ARCHERY
Wondrous item, uncommon (requires attunement)
so they have no such language attached to them, and do not state the arrows are magical.
The arrows themselves are also not a magic item, spell, spell attack nor are they fueled by spell slots, and the bracers do not make them any of that either, they just add +2 to damage. Ergo, they do not make the arrows magical.