Yes. Intensive fishing will exterminate the lot of them eventually. Otherwise, supply your water system from the brook/river via pumps and not natural flow. Powered off a water wheel, your only worry is winter ice. And that can be solved with some digging.
"Eventually" is a longer time than I'm willing to wait, at least without letting more dwarves than I'd like spend their days fishing. I still see salmon and shad blinking in and out, long after I got my system to work with bridge-gated "flood/drain latches" and fueled a couple dozen shallow magma workshops. The necessary 40+ round trips Z+139 to Z+6 took some time, but no overseer intervention once started (OK, I did have to help out with one manual load because magma evaporated from a double pit for adjacent magma forges, but that was error in execution not design [should have filled first tile 4/7 before channeling second])
Is fish extermination still a thing in 0.43.05? My reading of the wiki suggests fishable vermin spawn forever in wet places (in some areas, per PatrikLundell). Maybe those are just pond turtles and mussels that won't clog doors? Still, it seems sorta exploity or at least less than reliably short time.
Using bridges for "input" gates to flood/drain latches works fine with transient minecart-passage switch signals. Appropriately mixing retracting bridges and drawbridges also adds flexibility. Doors and floodgates only open and clear drainage volume on rising signal (Foff->Ton) and close without flow effect on falling (Ton->Foff) signals, respectively. Drawbridges add flexibility to open or close on either signal; they destroy water to clear drainage volume on a falling signal.
Elevation view
w=water, x=floor/wall,
S=Switch, R=Retracting bridge (no floor),
D=Drawbridge (raised side), d=drawbridge (lowered extent)
T:T
w R x x
x S R x
x D d x
x x x x
F:F
x w x x x
x D S D x
x x x x x
Bridge left or above switch is the flood input gate. Bridge(s) right or below switch is drain input gate. Combine desired form of input gates to build F:T or T:F latch
Lacking zero weight in their range settings, on arrival creature/cart switches can only trip OFF->ON not ON->OFF, so they're really only useful for active-T latch input gates. The latch flood input is simple enough active-T or active-F, but active-T drain input needs two bridges and invades another Zlevel.
Fluid level switches (water or magma) can be inverted by appropriate choice of range, e.g. 0-4 vs 5-7, which is why I call the latches "flood/drain" rather than "set/reset". A remote sensor that switches OFF at the desired level allows the simpler drawbridge F latch drain gate. The latch flood input overrides the drain input; choose high or low level for the latch switch accordingly.
Timing effects aside, it seems to me that switch *transitions* (ON<>OFF), not *levels* (ON or OFF), are all that really matters. A switch or lever steadily ON or OFF does nothing to hold an item state (e.g. open or closed); the item will respond when any other linked trigger *changes* to the other state (after the item's inherent delay from its last action). This wasn't clear to me from reading the wiki, but I'm demonstrably none too bright.
My magma lift proof of concept works. It takes a while to run using a single minecart, but still faster (for the dwarves) and much less tedious (for the overseer) than ordering load by load or powering a massive pump stack. Another minecart route can be overlaid, but the control system risks failure (actually intolerable delay and single dwarven death;
c'est la vie) if unfortunate (but likely) timing brings a cart to the loading pit at the wrong time in the other cart's sequence. If I can work out a way to sequence carts on overlapping routes, it can be made much faster. Film at eleven.