I wouldn't, just because the plants would put all that effort into growing new roots (and possibly twigs) that have a good chance of dying over winter. They don't get a chance to harden off. Does that make sense?

As a rule you should avoid fertilizing most plants after August in your zone so the plants all have time to prepare for their winter rest. This rule, like most any gardening rule, has it's exceptions. Turf grass is an obvious exception. Fertilizing them too late in the season, like Firethorn said, encourages new growth and new growth is less winter hardy. It also delays the main plant from preparing itself for dormancy.

Something that you can do during transplant though is amend the planting area with compost. This conditions the soil as well as provides a small amount of nutrients. Unlike most ferts, compost generally will not result in the plant being 'forced' to grow. The nutrients will be made available to the plant as it needs them.

Actually, current horticultural practices recommend fertilizing established woodies (trees and shrubs) in fall as this is the time when most plants are best able to metabolize nutrients via warm soils and actively growing root systems. Correct fertilizing does NOT encourage rampant lush growth which can be damaged by early frosts nor does it delay normal dormancy processes.

However, this pertains primarily to woodies and to already established plants. It is never a good idea to immediately fertilize newly planted material or those which have been recently transplanted. These plants are already in an ajustment period and unnecessary fertilizing simply places them under further stress. Suggestions to mulch with compost or other high quality organic mulch are very much on point. Mulching provides all sorts of benefits and the slow breakdown of the modest amounts of additional nutrients these materials provide and the added protection through winter will get these plants off to a good start in their new location.