Yes, but not because they can't. Not if they are true believers. Many have been taught from birth that tongues are not for today, or are around those who have this false teaching, and that puts a seed of unbelief in them, enough to quench the operation of this ability.
There is no such thing as a Christian that is not Spirit-filled, but many do not have the second filling for the gifts and boldness, but have the Spirit for the removal of the sin nature. That trumps all the manifestations of the Spirit. But tongues (prayer language) is in the first filling, and is part of the whole armor of God. The gift of diverse kinds of tongues that is for the profit of all, and must be accompanied by the gift of interpretation is what is given in the second filling.
In Acts 2 the apostles seem to be off to the side as they explain what is happening with the 120. They already received the first filling in John 20. On the Day of Pentecost they received the second for boldness and for supernaturally proclaiming the meaning of Joel 2. The 120 who received the first on the Day of Pentecost, received the second in Acts 4.