Are there helicopters with vertically mounted turbines?
Discounting the V-22 Osprey and the other tiltrotors, the drawbacks are:


Wasted cabin space
L-duct inlet(s) needed to guide the air in
With that potential problems with getting the air in as the air prefers fewer turns
A reduction gearbox is still needed
Gearbox still needed for the tail rotor
Harder maintenance access as it will be buried into the fuselage
If the exhaust is channeled downwards: potential tarmac melting, fuselage weakening, and handling issues in low hover
If channeled upwards, well, that's where the rotor is
Otherwise, extra heat ducting needed, i.e., added complexity and weight and expensive materials
Any fire or uncontained failure will cause grave danger.




Below is the best illustration I could find, and it gives you an idea about the previous points:


http://www.melm-md.com/images/N600_image_02.jpg