Can I run Pentair Pump without cartridge filter?

[mas985]

Can I just remove the filters and run without them while I circulate the chemicals to kill the algae?

Yes

A follow-up... Has anyone tried attaching a hose to one of the outlets of the cartridge tub so that I could vacuum the pool to waste?

I haven't myself but I know of someone who has done that so I know it can be done. How effective it may be is another issue. I think it would be better to have a three way valve between the pump and filter so you can direct all the flow to waste.