Many commentators seem to think so.
Matthew Poole: “In which, after ye were illuminated; in which they were convinced of the truth of the gospel, and received it in the love of it, and externally professed it, by being baptized into Christ, and by it made members of his church, Hebrews 6:4, and testified the truth of their being Christ’s.”
John Gill: “in which after ye were illuminated, by the Spirit of God, to see their impurity, impotence, and unrighteousness, and their lost and miserable state by nature; and to behold Christ and salvation by him; and to have some light into the doctrines of the Gospel; and some glimmering of the glories of another world. The Syriac and Ethiopic versions render it “baptized”; now such as are converted, and are brought to make a public profession of their faith, and submit to the ordinances of Christ, are, in common, immediately called to suffer reproach and persecution of one kind or another; so Christ, after his baptism, was led into the wilderness to be tempted by the devil: Satan is spiteful and malicious, and God suffers afflictions to befall his people to try their graces, and to inure them to troubles early, as follows;”
Pulpit Commentary: “Once enlightened” denotes the first apprehension of the light, which could be but once; when those that saw not began to see (John 5:39); when the light of the gospel of the glory of Christ shone once for all upon believers (2 Corinthians 4:4); when (according to the cognate passage, Hebrews 10:26; cf. Hebrews 10:32) they received the knowledge of the truth. . . . But, if so, more is meant by the phrase than “those who have been once baptized:” an inward spiritual illumination is plainly pointed to; and it would not have been said of Simon Magus that he had been “once enlightened” in the sense intended. And this is indeed the real meaning of φωτισμός as applied to baptism by Justin Martyr, as his explanation, above quoted, shows. So also Chrysostom (‘Hem.’ 116.), “The heretics have baptism, but not enlightenment (φωτισμα); they are baptized indeed as to the body, but in the soul they are not enlightened; as also Simon was baptized, but was not enlightened.” This consideration is important in view of one misapplication of the passage before us, which will be noticed below. But, further, those whom it is impossible to renew unto repentance are supposed not only to have been enlightened, but also to have “tasted of the heavenly gift,” the emphatic word here being apparently γενσαμένους: they have had experience as well as knowledge (cf. Psalm 34:8, “Oh, taste and see that the Lord is good;” and 1 Peter 2:3, “If so be ye have tasted that the Lord is gracious”). The word “gift” (δωρεά) is elsewhere used both for that of redemption generally (Romans 5:15-17), and especially, and most frequently, for the gift of the Holy Ghost (cf. 2 Corinthians 9:15, “Thanks be to God for his unspeakable Gift”). They have become also partakers of the Holy Ghost, not merely been within the range of his influence, but actually shared it; and tasted . . .