While there may be a start-up load for the heater's blower (fan) motor, there is also a higher start-up wattage for the pump motor as well - and that's the one I would be more concerned about. Sometimes, the start-up wattage on an electric induction motor can be up to 3 times the listed operating wattage of the motor. The start-up wattage usually lasts for a few seconds and, for this reason, circuits have a time-delay before tripping to allow for this very temporary higher than normal amp draw during start-up. If both the pump motor and blower start up at the same time the breaker could trip - it depends on the breaker and the wiring as well as the efficiency of both motors.
You need to know the wattage of both the pump motor and the heater's blower motor. Both should have a label indicating either the wattage or the amp draw at a given voltage (usually 115/120V or 230/240V). This will help determine if the current 20 AMP circuit is sufficient for both devices.
Keep in mind that the electrical load that a circuit can safely handle is determined primarily by the wire gauge and the line voltage. The breaker is a safety device that shuts off the circuit if the amp draw exceeds what the wiring can accommodate. It is vital that the breaker is matched to the voltage and amps that the installed wire gauge can handle. If the breaker is over-sized for the existing wiring, that is asking for trouble in the form of a fire risk. Conversely, a smaller breaker installed on a circuit that has the capacity to handle more amps increases the likelihood of "nuisance" tripping (this is conceptually how the 1965 NYC-East Coast blackout occurred - but that's another talk show).
If any of this sounds even remotely unclear, I would recommend hiring a licensed electrician to make the determination as to how these devices should be wired up. In addition, he/she will be aware of any local codes, aside from amp draw concerns, that may dictate how these items should be wired up. They will also check the existing circuit wiring and make sure that it is properly breakered. If you inherited the current setup, an electrician's expertise on this alone would be worthwhile. Many people take the cheap route by installing a breaker that is too large for the existing wiring and this is not something you want. Electricians I have talked with over the years state that they see this a lot.
