Yes, you need a transmitter, if you take that approach. That would be quite wasteful, if that is the only reason you get the transmitter. I would suggest instead building one of the 555-based servo drivers. At a minimum, it is good practice, and if you get into RC or robotics, they are invaluable for setting up servos.
With an ESC, it is hard to see what the driver is doing, unless you have an oscilloscope. So, for a few dollars more, get the cheapest servo the shop has. You can use that to be sure your servo driver is working. If you can find an older modeler, most of us have many used servos that we will never use. Some are new, but not of the quality we want. I give them away. Ask a shop where the modelers are and then make contact. If you were in Cleveland or nearby, I would give you one.
In summary, make a servo driver and test it with a cheap servo. Then use that to drive your esc.
Edit: Oh, I see you are in San Diego. That is a hot bed of RC activity. Definitely, ask the shop about a local club and make contact.
John