It's interesting that this question even gets raised since the very essence of "prayer", at least in biblical terms, is something offered to God the Father. The Father is, after all, the one who answers prayer. Paul said, "For all the promises of God find their Yes in him. That is why it is through him that we utter our Amen to God for his glory." (2 Co 1:20) Is that not abundantly clear? Who does Paul say we pray to? God. Why? Because He's the one from which all blessing flow.
It's the Father throughout all time up until Jesus' time on earth that all prayer was unquestionably offered to...So that when the disciples asked Jesus "teach us how to pray" (Lk 11:1-4), Jesus' answer is a prayer TO God the Father. Note that he doesn't say, "Hey, by the way, you can also pray to me." (And just think about him even saying something like that?? Can you imagine? Talk about usurping authority.) If once isn't enough, in a second place when teaching the multitude he says "when you pray...pray to your Father" (Mt 6:6) Sounds almost like a direct command right there....
Furthermore, we have the clear roles outlined for prayer. The Father hears/answers. The Holy Spirit helps our prayers (Ro 8:26). The Son is the authority by which we offer/ask...again, Paul "For all the promises of God find their Yes in him. That is why it is through him that we utter our Amen to God for his glory." (2 Co 1:20) And again, Jesus' own instructions on prayer, "In that day you will ask nothing of me. Truly, truly, I say to you, whatever you ask of the Father in my name, he will give it to you." (Jn 16:23)
Jesus literally says, "In the day you will ask NOTHING of me..." He gives instruction that prayer is to the Father (Mt 6:6, Lk 11:1-4). We have example after example and statement after statement about Paul and his own prayers - all to the Father (Ac 12:4-5, 16:25, Phi 1:4, Eph 3:14-15, Eph 5:18-21, 2 Ti 1:3, 1 Tim 1:12-14, 2:5-6, 1 Co 1:2, Ro 1:8-10, 2 Th 2:13-14, 2 Co 1:20, Col 1:3).
All that to say this in answer to the question. No! Paul was not praying to Jesus in 2 Cor 12. Based on Paul's own instruction and repeated examples of prayer, I'm pretty sure he would not contradict himself. Nor would he do something against Jesus' own instruction.