Short answer. Yes. Rule 45, Section 1 expressly states that a petition for review on certiorari to the Supreme Court "may include an application for a writ of preliminary injunction or other provisional remedies." You may also seek the same provisional remedies by a separate verified motion filed anytime while the case is pending.
What the law says
The petition may include an application for a writ of preliminary injunction or other provisional remedies and shall raise only questions of law which must be distinctly set forth
Rule 45, Section 1 — Filing of petition with Supreme Court. Read the full provision →
What the law says
The petitioner may seek the same provisional remedies by verified motion filed in the same action or proceeding at any time during its pendency
Rule 45, Section 1 — Filing of petition with Supreme Court. Read the full provision →
What a Rule 45 petition is
Rule 45, Section 1 describes the petition itself: "A party desiring to appeal by certiorari from a judgment, final order or resolution of the Court of Appeals, the Sandiganbayan, the Court of Tax Appeals, the Regional Trial Court or other courts, whenever authorized by law, may file with the Supreme Court a verified petition for review on certiorari." That petition is also where the rule addresses provisional remedies, including preliminary injunction.
The preliminary injunction option, in the petition itself
The very next sentence answers your question directly: "The petition may include an application for a writ of preliminary injunction or other provisional remedies and shall raise only questions of law which must be distinctly set forth." So the same document you file as your Rule 45 petition can also carry your application for a preliminary injunction — you are not required to file it separately, though the petition still has to be confined to questions of law.
You can also ask for it later, by separate motion
The rule does not require you to decide everything at the outset. It also states that "the petitioner may seek the same provisional remedies by verified motion filed in the same action or proceeding at any time during its pendency." So if you did not include a request for preliminary injunction in your original petition, the rule still lets you seek it afterward, through a verified motion, for as long as the case remains pending.
The petition's own limits still apply
Asking for a preliminary injunction does not loosen what a Rule 45 petition is otherwise allowed to raise. The rule ties the application for provisional remedies to a petition that must "raise only questions of law which must be distinctly set forth." A request for preliminary injunction rides along with the petition; it does not turn the petition into a vehicle for reviewing factual findings, which remains outside what this rule allows.