Yes geysers can and have burst.
Geysers bursting doesn't happen all that often but they do sometimes burst if they reach a hot enough temperature and have enough pressure built up.
The Geysers will sometimes burst when the geyser becomes super heated up and pressurized.
Then after the geyser builds up enough pressure the super heated water will overcome the weight of the overlying rocks and burst out of the ground in an explosive steam eruptiona geyser.
So you need to be very careful around geysers because they can erupt without warning and then the super hot water from the burst geyser can scald and burn you severely.
So watch geysers from a distance for safety.