Is the statement: "My Lord, I desire to go to Hajj. O Allah, cure me so that I can pray in the mosque in congregation, and so that I can go to Hajj" considered a vow, and is anything incumbent upon me if I am cured but do not go to Hajj?

The phrase mentioned is not a vow, for a vow is when a person obligates themselves to perform an act of worship that is not otherwise obligatory. What the questioner mentioned is a supplication, not an obligation. If the Hajj was supererogatory (nafilah), then there is no blame in not going after recovery. However, if it was obligatory (fard), then it remains obligatory when one is able.