Hi Craig, the pump may work to start with but it won’t be able to cope with this for long and will burn out.
I've done this before and it did work fine for a good while. I just removed the water container from the back pack and attached the water tank outlet and the hose reel inlet and kept the base of the back pack complete so I could use the built in flow controller. Another benefit in the winter was you just disconnected the whole unit and put it in the house to charge up like using a pump box. No freezing problems.
Would a Gardner backpack pump have enough power if I attached it the the end of a 100m reel?