The text states:
At 1st level, you gain the ability to imbue magic into a weapon or
armor. At the end of a long rest, touch one nonmagical object that is
a suit of armor or a simple or martial weapon. Until the end of your
next long rest, the object becomes a magic item, granting a +1 bonus
to AC if it’s armor or a +1 bonus to attack and damage rolls if it’s a
So, yes, the object is magical in nature, because it is a 'magic item'. However, it is not a +1 weapon, it is a magic weapon with +1 to rolls. The closest this is similar to is the 2nd level spell magic weapon. On that note, that would suggest this ability resembles the school of magic of transmutation, not enchantment, except Detect Magic's description says
If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
And this has no school of magic, because it's a class feature. In addition, Detect Magic doesn't detect the duration of the magic on the item, merely that it is, in fact, magical.
As a DM, I might rule that a character proficient in Arcana checks might be able to tell that it isn't a +1 weapon, (remember, magic weapon exists as a spell, so this scam is probably common), certainly, say, an Artificer, but anyone without experience in magical items wouldn't be able to. On that note, since it's a Cleric ability, someone with Religion proficiency would also be able to tell the object's true nature.