After the deadline, there will still be a delay after a DFA - not a 7-day period, but a club will still need to request waivers (whether outright or release), and the player will be in "limbo" until the claiming period expires.
Now, clubs do not have to DFA a player before they request waivers - that's always been the case. The DFA allows them to clear a roster spot immediately, without waiting for the waiver claim period to expire. The principal difference after 4 pm tomorrow is that there won't be much point in waiting several days to request waivers... although it's not clear to me that the DFA rule has actually been revised to eliminate the 7-day period to "dispose" of the player. Back to the Rule Book...
OK - There is nothing in the Rules to suggest that the 7-day DFA period is shortened after the Major League Trade Deadline.
Additional discovery: No player who signed a major-league contract (including players who have been outrighted) may be traded to another club between 4 pm on July 31st and the day following the last game of the World Series. No loophole there. This is Rule 9(b)(3).
Rule 9(b) also restricts trades of minor league players to a major-league club - but only in the last week of the regular season through the post-season. Then there's also a provision that allows the Commissioner to void any transaction, or series of transactions, that appears to be designed to circumvent the trade deadline.