The answer is no. The reason is this. The Church teaches that to partake of Communion in any Christian tradition is publicly to declare one is in full agreement with what that tradition teaches or holds. Therefore, if you, a Catholic, were to share in the Communion of a non-Catholic tradition, your action would bespeak a falsehood.

For the same reason, the Church does not allow non-Catholics to receive the Body and Blood of Our Lord in the Eucharist. This prohibition has nothing to do with the spiritual state of non-Catholics. In fact the rule exists for the protection of the integrity of non-Catholics who happen to be present at a Eucharistic celebration. It prevents them from unwittingly, but still symbolically, making a public statement that is untrue.