Assuming you're running at 125 power, no, adding a 4th DHC won't hurt your DPS. What it WILL do is lower your spike damage potential, because Torpedos give you more options versus Hull via both HYT (ST) and TS (AoE).
I'll just add my little anecdote.
In an Escort on ESTFs, I've switched from 3 DHCs + 1 Torp to 4 DHCs.
The DPS with this set up is higher than any other set up I've run (which includes 2 Torps + 2 DHCs and 3x Purple PWOs).
Part of that increased DPS just goes to the overall efficiency of the build - all of my consoles are 1 Energy type and not having Torps means I can squeeze in multiple Attack Pattern Betas.
On the other hand, even with this much better DPS - which I tend to notice against enemies like negh'var and cubes/elite cubes the most - the lower spike damage is apparent as maelwy5 has stated.
So while the consistent DPS is very high, doing something such as Guarding Kang or working both sides of KASE (1 ship, covering both sides) can be slowed down a touch (it is by no means hard with a Tac in Escort but it's definitely not as efficient as having 1 or 2 torp launchers for those circumstances).
Probe and Kang duty tend to bore me to tears, so I tend to avoid those unless no once else has a ship capable (rare).