You are not going to catch me worshipping one or the other in a pantheon of lesser gods.
So "constant" - I don't know. God could be constant, or He could elect to be otherwise. As far as "prayer" representing worship of this, that or another god, it might, or it might not. If words have binding power over God, then it's a real issue; otherwise, with an omniscient God, He'll know who has a legitimate prayer and who doesn't.
And that takes us right back to the Priest, Melchizedek in ancient times. Was he, in fact, a manifestation of the Triune God, or was he merely a man? Jesus references to Him are quite interesting, and I don't think Calvinists or Lutherans, or Catholics, or Moslems, or Hindus, or Buddhists, or any other variety can move the issue ahead until we get a clear understanding of Melchizedek!
The question of Melchizedek is really an interesting one and one I do not, for one moment understand. If I remember, however, the LDS church have a theory on that. I do not remember it completely so won't try.
I thought I'd heard it all, but to know now that God will not listen to any prayers but the Fullly Immersed fundamentalists, now there's a new height. For fun, I like perusing the Landover Baptist site.