Why not? Asexual people can have multiple romantic partners and may never engage in sex.
I think it is totally possible to be romantically in love with people and not engage in sexual activity. The love is the same but the expression is just different.
For some this would be frustrating, for an asexual person this would be completely adequate. For a person with boundaries around physical partners it might only be tolerable.
You don't even need to include poly in this question because the same principle would apply to a romantic but non-sexual monogamous relationship.
Getting to know asexual people has really changed my view on love and sex.
Playing the Game of Life with Monopoly rules.
Monogamy might just be in my genes
Poly Events All Over