Yes two hurricanes/tropical cyclones/typhoons can merge with each other and the effect is known as Fujiwhara effect- Fujiwhara effect.
The National Weather Service defines the Fujiwhara effect as "Binary Interaction where tropical cyclones within a certain distance(300-375 nautical miles depending on the size of the cyclones) of each other begin to rotate about a common midpoint". What really happens is that centers of both systems begin to orbit in a counter clockwise direction about a midpoint that is determined by the relative mass and cyclone intensity. Eventually the smaller cyclone may merge into the larger cyclone.
There are several examples of the Fujiwhara effect and one example would be Hurricane Connie Hurricane Connie and Diane Hurricane Diane way back in 1955. Shimokawa et al Fujiwhara Effect Types talk about the various kinds of interactions that can take place among various typhoons(Please note that the Fujiwhara effect is not restricted to two systems). The various kinds of interactions are
- Complete Merger
- Partial Merger
- Complete Straining Out
- Partial Straining Out
- Elastic Straining Out
Complete straining and complete merger interactions lead to destruction of one of the vortices. Partial merger and partial straining lead to partial destruction of one vortex and elastic straining is an interaction in which both vortices survive with their initial circulation. Partial merger and partial straining out have received less attention in the literature on binary tropical cyclone interactions as the interactions are extremely complex. Prieto et al claim that during a partial merger repeated mass exchanges occur between vortices. As these are nonlinear effects a quantification is only possible by a direct numerical integration and precise initial condition Binary TC Vortex Like Interactions
The period of orbit maybe as small as one day or there are others such as Cyclone Kathy and Cyclone Marie Kathy/Marie Fujiwhara orbited for a period of 5 days prior to merging into each other as pointed out by Lander et al. If the period of orbit is longer then there is a greater probability of a merger.
Region wise binary cyclones are more common in the Western North Pacific than the North Atlantic as pointed by Dong et al Relative Motion Of Binary Tropical Cyclones
Regarding the predictability of the track of binary cyclones Dong et al. state that prediction of steering forces of a single tropical cyclone are replete with numerical forecasting uncertainties and the problem is accentuated by the presence of another tropical cyclone in close proximity.
Those who followed the progress of Hurricane Sandy in late October 2012 (an instance of the Fujiwhara effect but in this case a tropical cyclone merged with an extra tropical storm) will remember the ECMWF model correctly predicted the landfall location.