Yes, occasionally God does grant some people a glimpse of heaven's glory, particularly as they near death. It is not common–but it does happen.
The Bible records a few instances of this. As he was about to be stoned to death because of his faith, we are told that Stephen (the first Christian martyr) "looked up to heaven and saw the glory of God, and Jesus standing at the right hand of God" (Acts 7:55). Such glimpses of heaven should not be confused with reports of a tunnel of light or other images that are reported from time to time, and may be invalid or even deceptive.
My own mother, in fact, believed she was given a brief glimpse of heaven shortly before her death. Not only did she sense heaven's glory, but she also saw some of her loved ones there. My mother had a deep faith in Christ and lived every day with a strong sense of God's presence. I am also convinced that, for her, the transition from this life to heaven involved only a very short step.
The most important thing to remember, however, is that we do not need to depend on such visions to assure us of heaven's reality. We know heaven is real because of God's promises, and because Christ died and rose again for our salvation. The Bible says, "For Christ died for sins once for all ... to bring you to God" (1 Peter 3:18). Have you committed your life to Him?