No... unless you used a silvered arrow.
Relevant parts of the spell:
You fire a piece of nonmagical ammunition from a
ranged weapon or throw a nonmagical weapon into
the air and choose a point within range.
The damage type is the same as that of the ammunition or weapon.
This is very, very clear. You use non-magical ammo, and the damage dealt is the same as the ammunition used. Which means it's non-magical.
There's also precedence that just because magic creates the damage source, it doesn't mean the damage is automatically magical. For example, Create Undead makes minions for you, but their attacks do not count as magical unless their stat block specifically state that they do.
Here's a comparable spell that takes a mundane weapon and makes it magical:
Shillelagh, PHB pg. 275 (emphasis mine);
The wood of a club or quarterstaff you are holding is
imbued with nature’s power. For the duration, you can
use your spellcasting ability instead of Strength for
the attack and damage rolls of melee attacks using
that weapon, and the weapon's damage die becomes
a d8. The weapon also becomes magical, if it isn’t
already. The spell ends if you cast it again or if you let go
of the weapon.
This is how you know if your spell counts as magical. It will explicitly state it in the description. If it doesn't, the damage type is NOT magical by default. Conjure Volley and Conjure Barrage lack this statement, so their damage type is NOT magical in nature.
Here's an example of a spell that creates ammo for you that is not magical:
Swift Quiver, PHB pg. 279-280 (emphasis mine):
You transmute your quiver so it produces an endless
supply of nonmagical ammunition, which seems to leap
into your hand when you reach for it.