The power requirement curve for an axial flow fan is not the same as a centrifugal fan for sure, it is flatter, even more skewed to being the OPPOSITE of a centrifugal fan depending on the pressure requirements it is used for. So from that standpoint, it is a "constant torque" looking application.
But from the VFD standpoint, the term "Constant Torque" and "Variable Torque" really is a misnomer, because the VFDs are CAPABLE of delivering either. The terminology for VFDs has to do with the OVERLOAD capacity of the drive itself. So because it is virtually impossible for a true centrifugal machine to overload the VFD at reduced speeds, there is no need for the VFD to be sized to deliver that overload capacity, hence we call it a "VT" or "Pump / Fan Duty" drive and up-rate the HP capacity. From that aspect, an Axial Fan is the same as a Centrifugal Fan, you cannot overload it, so the VFD does not need to be capable of the added OL capability inherent in a "Constant Torque" rating.
Bottom line, you can use a "Variable Torque" / "Fan and Pump" / "Normal Duty" rated VFD on an axial flow fan.
The same is not true of Axial Flow PUMPS, by the way, and may be what is behind your thoughts. The difference is, liquids can't compress like gases (air), so a flow restriction in an axial flow pump CAN result in an increase in load of the pump, so the VFD must be sized for that.