They don't anything for counterbalancing the weight of the sash, which can be pretty significant when you open or close the window. They are a step up from the "nail in the frame" approach.

Depending on where you are replacing the sash cords and weights isn't a horrid experience. If you're lucky, the original weights are still in the pockets. Have you considered that approach?

I have fixed a few sash cords, but eventually I want to fill in the pockets with insulation and use the spring balances by Pullman. I was wondering if these sash springs would buy me a couple of years until I can afford spring balances, but would also allow me to get started with the insulation.

It sounds like you think the tension the springs provide isn't enough for the weight of a wood sash.

They will probably hold them in place just fine.

My concern stems from knowing how unwieldy the sashes are in our Victorian when even one weight is disconnected. I've banged too many fingers and lost panes of glass as a result of unbalanced sashes.

Spring balances vs. weights is a personal choice based on cost and a desire to stuff insulation in the gaps. Both should work fine, if properly sized. My personal feeling is that until you've put in some kind of weatherstripping to seal the sashes to the frame, the heat losses through the sash pockets are pretty small compared to the infiltration around the sashes.