Not automatically, but you have advantage on persuading them otherwise
The charmed condition states merely two effects:
- A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects.
- The charmer has advantage on any ability check to interact socially with the creature.
So it guarantees they won't attack you, and makes them much receptive to your attempts to interact with them, but it doesn't guarantee that they automatically consider you an ally and will willingly submit to magical effects. It also has no effect on the subject's interaction with other creatures, such as your other allies - being "charmed" only affects how the charmer and charmee can interact.
However, the spell Charm Person also clarifies that:
The charmed creature regards you as a friendly acquaintance.
This seems much closer to being considered an "ally", but in my opinion it's still not quite all the way there. Rules as written, I don't think a creature subject to charm person should automatically count as an ally.
However, they are friendly to you, regard you as an acquaintance, and you have advantage on social rolls. I would personally rule that you could readily attempt a quick Charisma (Persuasion or Deception) check against the subject's Wisdom (Insight) to try and convince them that they should totally let you do this magical thing to them (or that they should let your friend here cast this spell on them), and you'd get advantage against the charmed target - so you can convince them that they should consider you and your party to be allies.