Incantatrix, spell-selection, and metamagic feats are the heart and soul of the mailman. The remaining class levels are not important, and could be archmage levels. In other words, you definitely can do it. Just take the feats and spells you need and have at it. You’ll still be phenomenally powerful.
That said, there is a problem. The problem with this is that archmage is a difficult class for the sorcerer to enter, and its most useful effects aren’t exactly stunning for the mailman build.
First, entry. Spell Focus in two schools is useless to a mailman because a mailman doesn’t want spells that allow saving throws; giving your opponent a chance to prevent you from delivering is the antithesis of everything the mailman is about. Skill Focus (spellcraft) is worthless to just about everyone. Finally, the spell requirement could be very harsh: sorcerers have a hard enough time choosing spells, having to arbitrarily “hit” five different schools with your 5th-and-higher spells known hurts a lot.
Note that archmage is really a wizard prestige class, since wizards can be master specialists (using a Spell Focus feat for two different classes and getting the Skill Focus for free), and can also scribe as many spells as they want into their spellbook to hit all five schools. Sorcerers can enter, and use it well, but it requires some real dedication.
But as a mailman, that dedication and sacrifice to enter the class is not rewarded very well.
Mastery of Elements is solid enough, but between force-damage effects, and Energy Substitution and Searing Flames or Piercing Cold, a mailman shouldn’t need it; very few things are immune to force damage and nothing is immune to Searing Flames/Piercing Cold.
Mastery of Counterspelling is weak because counterspelling is weak. As a mailman, you should not going to be readying spells to counterspell, because you can do so much more with your standard action by just nuking it to hell. That’s what you do, and you do it very, very well. No need to counterspell if the spellcaster is already dead. A dedicated counterspelling build is not compatible with being a mailman, and is ultimately lackluster.
Mastery of Shaping is worthless to you because you are about the single-target nuke, not area-effect. Area spells invariably offer saves, which are not your game. Still, this is a powerful effect, and worth picking up for situational use... if it weren’t for how painful being an archmage is to begin with.
Arcane Reach is actually excellent for you, and ultimately what may make the whole thing worth trying. If you are starting at 17th level, designing your build around getting this could work really well. But if not, you cannot afford to wait until you get it, and sitting around with spells and feats you don’t want so you can enter archmage in several levels would be extremely painful.
Arcane Fire is garbage and you do far more damage with those spell slots than it ever can, Spell Power is nice but too small a bonus to justify entry, and Spell-like Abilities cannot be augmented with metamagic so that option is just worthless to you.
All that said, a note on counterspelling and the mailman. As noted, it’s not worth it to ready an action to counterspell when you could just kill the caster. But maybe you find something you can’t kill in one shot, and letting that character get even one spell off could be your doom. A high-end fiend while you’re still in middling levels, perhaps, where it can soak the damage and respond with blasphemy.
In this situation, a mailman doesn’t counterspell, per se, but rather counter-nukes. This is a brutal tactic that I recommend you keep in your back pocket for a truly dangerous occasion, because using it too much might have enemies using it on you, and you don’t want that.
The way it works is, you ready an action for when someone casts a spell, just like you would if you were counterspelling. You don’t ready a counterspell, though: you ready a nuke. Your most reliable, hardest-hitting nuke. When they cast, you nail them with this, and not only do they take a ton of damage (that’s what you do, after all), but they also must make a ridiculous Concentration check or lose their spell.
The best part is, this works on almost anything. Any spell, power, mystery, even spell-like abilities, all of them can be disrupted by getting hurt, and your nukes hurt a lot. Skill checks tend to scale quickly, better than +1/level, so usually making Concentration checks is easy. But when you hit for a hundred or more damage, and the DC 10+damage dealt? That check isn’t easy, it’s basically impossible.