UPDATE: See Space News' NASA tweaks call for lunar lander concepts which links to:
- FedBizOpps: Human Landing System - Integrated Lander
- NASA.gov: NextSTEP H: Human Landing System - Integrated Lander; Solicitation Number: NNH19ZCQ001K_APP-H
The question Has NASA “gone south”? Why are astronauts needed to explore the Moon's south pole? and its answers highlight the recent US executive branch's indeterminately-funded mandate.
As far as I understand, the gateway will be in the loop and a stop-over for the astronauts, and the reason I think so is that getting to the moon is the raison d'être for the gateway, so it would be awkward if it wasn't used. Or, to quote someone famous; "I don’t see any reason why it wouldn’t be (used)."
The exact propulsive scenario is still of course uncertain, especially the trip between the gateway and the Moon, but is it possible to estimate how many stages of propulsion the astronauts will experience on the round trip? How does the total number of propulsive stages compare to the Apollo missions?
In the Ars Technica's Here’s why NASA’s audacious return to the Moon just might work the subsection What hardware are they planning to use? outlines a notional scenario. This might possibly be useful as an example "notional" scenario from which to make an estimate.
See Ars Technica's in-depth article How much will the Moon plan cost? We should know in two weeks
From NASASpaceflight.com's NASA Launch Services Program outlines the alternative launcher review for EM-1, click for larger size: