Yes. This name "person" is fittingly applied to God because "person" signifies what is most perfect in all nature (that is, a subsistent individual of a rational nature) and everything that is perfect must be attributed to God (inasmuch as His essence contains every perfection): not, however, as it is applied to creatures, but in a more excellent way (as other names also, which, while giving them to creatures, we attribute to God).
Although the word "person" is not found applied to God in Scripture, either in the Old or New Testament, nevertheless what the word signifies is found to be affirmed of God in many places of Scripture: that He is the supreme self-subsisting being, and the most perfectly intelligent being.
The word "hypostasis" does not apply to God as regards its source of origin, since He does not underlie accidents; but it applies to Him in its objective sense, for it is imposed to signify the subsistence.
It may be said that God has a rational "nature," if reason be taken to mean, not discursive thought, but in a general sense, an intelligent nature. But God cannot be called an "individual" in the sense that His individuality comes from matter; but only in the sense which implies incommunicability. "Substance" can be applied to God in the sense of signifying self-subsistence.
There are some, however, who say that the definition of Boethius (Q29 A1) is not a definition of person in the sense we use when speaking of persons in God. Therefore Richard of St. Victor amends this definition by adding that "Person" in God is "the incommunicable existence of the divine nature."