If a given sequence is hard coded (ie as a fixed, Manchester Sequence) into a PIC ...
I think it's time to step back and look at the options and bear in mind what the problem is you are trying to overcome. That problem seems to be that you cannot SERIN wireless from a dumb RF module and reliably use timeout when there's no data being transmitted - that is correct.
The two options to overcome that are to use a second PICAXE or an NKM2401 receiver at the receiving end. There is no option which does not require two chips at the receiving end.
If you use another PICAXE the transmitters can be a single PICAXE using SEROUT direct to dumb RF modules.
If you use an NKM2401 the sending PICAXE will either have to support the RFOUT command or also use an NKM2401 transmitter to drive the dumb RF module.
The three main options you have are ...
SEROUT ---------------> TX ~~> RX --> PICAXE (SERIN) <==> PICAXE
RFOUT ----------------> TX ~~> RX --> NKM2401 <=======> PICAXE
SEROUT --> NKM2401 --> TX ~~> RX --> NKM2401 <=======> PICAXE
But you could replace the receiving NKM2401 with a PICAXE which supports RFIN ...
RFOUT ----------------> TX ~~> RX --> PICAXE (RFIN) <====> PICAXE
SEROUT --> NKM2401 --> TX ~~> RX --> PICAXE (RFIN) <====> PICAXE
You could program a PICmicro so it churns out a stream that an NKM2401 can read and understand ( replacing the transmitting PICAXE using RFOUT in the second option above ), but you would need to program a PICmicro for that and then use an NKM2401 at the receiving end. That doesn't seem to give any advantage I can see over using a PICAXE that supports RFOUT or the first option which can be implemented using off the shelf parts.