Yes it is very likely to work. ( It is OK to have more receiver channels than what your transmitter has ).

However I would STRONGLY advise you to try to get a transmitter with more channels.

You'll later be kicking yourself for not having done so... You will remember this exchange where I told you this.

More channels means that you'll be able to use the transmitter with other planes. Here are some examples...

5 channels may give you enough to handle a plane with retractable landing gear.
6 channels landing gear and flaps
7 channels permits the above with aileron differential
8 channels permits all of the above or quad flaps
9 channels permits all of the above and dual elevator servos
10 channels permits all of the above and/or handling the choke on a gas plane.

etc. etc.

It is better to start out with a quality transmitter, that will handle many different planes, and keep the settings for all of them, than to kick yourself for having limited yourself to 4 channels.

You can also sell a good transmitter later. Cheap ones are not in high demand.