Can a furnace with a variable speed blower be used in a multistory house?
Does the ratio of static pressures between two stories differ at different blower speeds? That's a very interesting question, but I believe it's a moot point. Any dramatic difference would mean your system isn't balanced correctly in the first place. (needs zoning, split systems, or an actual balancing)

Stack effect will cause plenty of heat to go upstairs, while the cold air will settle. I'd be more concerned that it won't cool right. Except that furnaces usually only run at high speed for AC because cold air is denser, making it harder to push. If your old system heats and cools just fine I don't foresee a problem.

Without being in the correct centralized location (which is somewhere on the first floor of a two story), the thermostat will not control the house properly. In low-fire mode, indeed less air will go upstairs and downstairs, per minute. Blowing softly is what makes it more comfortable. It will run longer and more often, reducing the intermittent temperature differential, keeping the house nice and even.

So no, the same amount of 'less' air will be coming out below as above. Your contractor either is trying to up-sell you into a split system (or knows more than I do) or convince you that zoning is required (a possibility, however this can be retrofitted later at your discretion). Either of these additions would dramatically increase the cost.

Unless your house has automatic zoning and was balanced by a genius, it will always be hotter on the second floor in the winter, and colder on the first in the summer, just like everyone else's.