Can molasses be applied year round or is there a time of the year that it wouldn't be beneficial?

Yes.. You can use it anytime because it feeds the beneficial microbes in the soil year-round!
Here is what Dry Molasses did for my front yard.
Before photo:


1 and 1/2 years later:


I fed it with "Soil Mender dry molasses" and Garret Juice. Nothing else..

A photo is worth a thousand words! {grin}
~N2O~