Absolutely. In fact, I used to play in a league for a club - I played for Keele University in the UK - and even in over the board games that would last 2-3 hours, at certainly points in the game my heart would be beating like a drum. It's one of the reasons I stopped playing in the league. People might think it is boring and sedate. Nothing could be further from the truth.
Does your heart also beat fast during a Blitz game?

yes especially when the game counts for something such as playing a titled player or a last round game of a tournament in a must win situation

Although it is fun and exciting getting those adrenalin rushes, i try to calm myself down when it happens because i tend to move too fast and have a harder time to observe the board properly.
A lot of people make fun of chess players, perpetuating the stereotype of the nerdy kid with glasses, but to me a serious Blitz game gives me an adrenaline rush. My heart starts pumping like crazy when a critical position is reached. Winning under immense time pressure is the same to me as submitting an opponent in jiu jitsu, one's more physical but the feeling is the same.
You win as many games as you lose. So, you must feel like someone has put you into submission frequently and experience a subsequent bad feeling.
A lot of people make fun of chess players, perpetuating the stereotype of the nerdy kid with glasses, but to me a serious Blitz game gives me an adrenaline rush. My heart starts pumping like crazy when a critical position is reached. Winning under immense time pressure is the same to me as submitting an opponent in jiu jitsu, one's more physical but the feeling is the same.