If you received a subpoena in the mail, you were not properly served and do not have to appear at court. A subpoena has to be hand-delivered to you directly. If the State is trying to get you to court, they are not going to arrest you for ticket warrants. If the defense issued the subpoena, the State may take you in on the warrants but it is unlikely.
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Yes, you can be arrested if they look up your criminal history and find you have traffic warrants.
If you received the subpoena by certified mail, you have been properly subpoenaed and you must appear or be subject to being picked up. (If you just received it by regular mail and do not appear, the party who issued it will most likely have you personally served next time....)