No, Jesus did not subject Himself to the law of the land by paying the temple tax.
For one thing, the temple tax (see Exodus 30:12 ff.) was not a law of the land, but it was a law of Moses imposed on the "sons of Israel" both as a ransom for them and for the maintenance of the "tent of meeting" (i.e., the tabernacle).
By paying the temple tax Jesus was avoiding unnecessary controversy and at the same time not offending the collectors of the tax, who were within their rights to do so (again, see Exodus 30:12 ff.).
We do well, however, to follow Jesus' line of reasoning for doing so, and the logic he used with impetuous Peter who took it upon himself to speak for Jesus when asked if his teacher (i.e., Jesus) paid the two-drachma tax. Here is what Constable says about this passage:
"Jesus turned this inquiry from the tax collector into a teaching situation for Peter and presumably the other disciples. Jesus changed the tax from a religious one to a civil one to make His point clearer. The principle is the same in both cases, but it was easier to illustrate in the civil arena of life.
Jesus’ point was that [just] as the sons of kings are exempt from the taxes their fathers impose, . . . He [too] was exempt from the taxes His Father imposed. He meant the temple tax. The temple really belonged to God (Mal. 3:1). Jesus was teaching Peter the implications of His deity. He was not teaching Peter to fulfill his civic responsibility [my italics].
"Even though He was exempt, Jesus would pay the tax because He did not want to offend anyone needlessly (cf. 5:29). Failure to pay the tax would create unnecessary problems. Because Peter was one of Jesus’ disciples and one of God’s children through faith in Jesus, he also had no obligation to pay the temple tax (cf. 12:1-8) . . .. Since the sons of God are exempt from maintaining the temple and its service, the end of this system of worship appeared to be approaching, as it was. Here is another indication that Jesus ended the Mosaic Law (15:11).
Jesus' paying of the temple tax for both himself and Peter was not an instance of Jesus subjecting himself to any law, whether imposed by the state or by God through Moses for Israel. Rather, paying the tax was a teaching opportunity through which he taught his disciples about his deity and specifically about his relationship to the Law and to the Law Giver.
In conclusion, it is said that no one is above the law. No one, that is, except the Law Giver. Some of Jesus' most memorable words began with the phrase,
"You have heard that it was said, . . .. But I say unto you . . .." (see Matthew 5:21 ff.),
and yet, the same Jesus also said,
"Do not think I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill" (Matthew 5:17 NASB Updated).
Christians thank God that though Jesus was above the Law, he also came to fulfill it perfectly for those of us who could not.