CAN it be done?
While I agree with Dan B that this would not be imbalanced for level 12 players, and I agree with you that physically, it can be done, but this begs the question; Where did the +1 come from, and can it be transferred?
I ask this because There are a couple of premises behind +x items;
- The item has been made with extreme craftsmanship for extraordinary effectiveness
- The item has been imbued with magic to make it more effective
- The item has been made with special materials that grant it extraordinary effectiveness.
Being adamantine, I feel we can easily strike out the third category, but if one of the other 2 are the reason for its bonus, you may have a problem.
If the item has been made with extreme craftsmanship
Then would coating it in another material make it less effective? Might adding hot metal remove some of the temper on the armor, or it might not fit the same? It would definitely be heavier by adding another coat of metal to it.
Is this player an exceptional armorer or blacksmith? If so, then these concerns are moot. If not, then I feel that you would lose the extra oomph that it being so aerodynamically crafted, with a fit so divine, and practical weightlessness that gives it that extra boost.
+1 can not be brought down, but if it were +2 or more, I would bring down the bonus unless the character in question had magnificent affinity for blacksmithing/armor making.
Neither you nor your player(s) may care about such things, but it is worth thinking about in my opinion.
If the item has been imbued with magic
Then which one are you destroying? It sounds like you're destroying the adamantine armor to add to the +1 armor. The other way around, is the item is destroyed, and the magic it contained with it?
I am currently unaware of any 5e rules for destroying magical items, but I am not the alpha-and-omega of 5e rules...
And a last thought to this; Would adamantine block the magic? Some spells are blocked by materials, i.e. Detect Thoughts states;
The spell can penetrate barriers, but 2 feet of rock, 2 inches of any metal other than lead, or a thin sheet of lead blocks you.<
Detect Thoughts DnD Beyond
Correct, nobody is likely to add two inches of adamantine to their plate armor under normal circumstances, but though adamantine is not magical, it does interact oddly with magic. For instance, the Gargoyle has this resistance;
Damage Resistances Bludgeoning, Piercing, and Slashing from Nonmagical Attacks that aren't Adamantine<
Gargoyle DnD Beyond
If adamantine can overcome nonmagical damage resistance, what might it do to the magic on the +1 armor that is now being coated with it?
Is your dwarf smith a caster? A caster who can handle 6th level spells (will be 7th level at 13!) should have the know-how to handle this situation. Maybe a few Arcana checks while it's being made, to be sure of proper focus (Religion checks if it's a religious caster rather than arcane)?
All that being said, I would allow it.
I like it, it's creative, it's personal, it's perfect! If a player told me they wanted to do this, I would build in the down time to do so. This is the kind of character engagement that should be rewarded. "I like this armor/flavor, but I don't want to lose this.
I like the 1,000 gold cost, and I would also say that it should be done in downtime. Unless you feel it should be, I see no reason to add penalties or attunement, as this armor has basically just adjusted to +1 Adamantine Plate Armor instead of the usual.