No, the number of channels of the receiver can be less than or more than the channels of the transmitter. It doesn't matter. The only thing you need to worry about, in general, is the frequency of the xmtr and rcvr and the shift. Some transmitters use a positive shift and others a negative shift. I forget which are which but you can go onto
www.servocity.com to find out.
My xmtrs are 9 channel and I use them with 5 channel receivers on up.