Plants definitely help in freshwater, regardless of if they're in the display tank or some other connected vessel. Many people just put them in the display, since they're beautiful and - of course - there's no corals in the display of a FW tank.
Establishment and cycling of a new FW tank can be similar to a marine tank, but given certain techniques, planted FW tanks can be handled far differently. Given a certain maintenance strategy, there's absolutely no reason to hold off on planting a FW tank, and in fact it can be beneficial to plant sooner rather than later. In a planted tank, the plants are absorbing nutrients from the water and substrate - they are effectively acting as a filtration (or, more properly, a nutrient export) mechanism. Hence, in the same way that you want to run your skimmer from day one on a marine tank, you want plants in a FW tank from day one.
I've established many planted freshwater aquariums over the years, and can confidently say that you can put plants in on day one. In fact, modern practice more or less calls for stuffing the tank with plants right from the beginning - this way, they establish themselves and outcompete pest algae for nutrients and light.
These tanks are also typically fed CO2 (to provide a carbon source), liquid or powder fertilizers (containing the three macro nutrients and proper trace elements), and strong light (strong for a FW at least - even the strongest planted tank lights are at best average compared to reef lighting rigs.) In this sort of tank, many species of plants will thrive and grow to the point that huge weekly trimmings are required.
Clearly, this is a different approach than the typical mixed-purpose tropical FW tank, and requires careful planning and knowledge to pull it off - but it is certainly an accepted and well-proven method.
Some good reading:
www.plantedtank.net
www.aquaticplantcentral.com
Here's a (crappy cell phone) photo of a planted 60g tank I had running a few years ago. At it's peak, I'd pull out a big mixing bowl full of trimmings every week:
Plants were in the tank mere hours after it was filled with water and brought up to temperature. It had three VHOs, CO2, and was fed a few times a week with a fert mix I made from bulk sources. There was a big canister filter on it, but honestly it was only really necessary for water movement - the plants did such a good job of pulling nutrients out of the water, there really was no other filtration or nutrient export needed.
