Yes it definitely does, the best advice is always to negotiate price before incentives and trade. I typically talk to sales person in terms of a function of invoice (below invoice by x%). However, even after all of these once you mention a trade they will factor in the price they quoted you.
For example on the 2019 I ordered a couple weeks ago my negotiation went as follows. Dealer knows at worst I get Chrysler affiliate pricing (1% below invoice), however i typically buy Invoice minus the holdback (3% of MSRP). With this deal they quoted me affiliate pricing minus the holdback, which put me ~6.5% below invoice. This price was ~$400 above EP. Once we had this sorted out we talked trade, the negotiations landed me about $500-$750 above below where I wanted to be on the truck, but I was ok with this because I was already just above EP pricing.
Also, I Just got one of those $500 mailers, which expires on 7/2, so keeping my fingers crossed I get my truck in time.