Mmmno. 1hp = 550ftlb/s. It's defined as the amount of power required to raise a mass of 550lb through one vertical foot in one second.
I'll still respectively disagree

Well, maybe, I'm not sure how "units" are defined.
Power, regardless of what units you define it as, has dimensions of length*force/time. That doesn't mean horsepower has units of ft·lbf/s. It'd be like saying 60mph has units of metres/second because you can convert it to metres/second. They both have the same dimensions, length/time, but the units are different and separated by a constant of 0.447.
Like if I have a glass of water next to me. I shall define the volume of liquid as being 1 glass. It has dimensions of length^3 by definition that it is a volume. But its units are ambigious, it could be defined as 562 millilitres, 0.148 gallons, 2.37 cups... they all mean the same thing.
Does that mean a "glass" has units of millilitres, gallons or cups? Or none of the above? I dunno... personally I'd say it is none of the above, yet via a conversion through multiplication by a constant, it can have any of those units

Maybe I'm wrong.
Horsepower is the same deal... it is defined as 550 ft·lbf/s, or 746 watts (N·m/s). Does that mean it has units of ft·lbf/s or N·m/s? Well, in my opinion it has neither, simply that it can be expressed in units of either ft·lbf/s or N·m/s through multiplication by a constant.
Hence why I said previously you need to multiply hp by 550 to convert it to a meaningful unit.
If you divide 1hp (550ftlb/s) by the constant 550 you get 1ftlb/s. If you divided it by a quantity, say 550 seconds, you'd get 1ftlb - which is a unit of torque.
I'm not sure of the significance of what you're trying to say, I'm not talking about torque, just power
Also your example looks wrong... power has dimensions length*force/time, if you divide it again by time you'd have length*force/time^2 while torque should have dimensions of length*force

I think you mean divide by a rotational speed, 550 rad/s... or maybe you meant multiply by a time to get an energy.
I can't believe I just spent that long talking about units and dimensions... that's what happens when you're stuck at home, sick, with nothing better to do. Its going a smidge off topic, my apologies. I wont reply again, I promise.
EDIT: Do you work as an Aerospace Engineer at Kennedy Space Center?