That's a very complicated location specific question. Over fishing herring can certainly have an impact on all the predators that feed on it including salmon.
That being said when there's an abundance of herring I don't see anything wrong with having a commercial fishery for them.
The problem tho is our managers are not necessarily the best at predicting what the impacts will be or at what level that can be sustain harvest.
We are also living in a time with high uncertainty, Climate change and then also banning the harvest of predators such as humpback whales. A lot of the commercial harvest is being replaced by growth in predators populations such as seals and humpback whales.
https://www.sciencedirect.com/science/article/pii/S0967064516303174
"While the increase in humpback whale numbers in the North Pacific is a success story (
Barlow et al., 2011), it may be having an effect on its prey populations. Furthermore, as humpback whales continue to recover globally, perhaps to above pre-whaling levels (
Ivashchenko et al., 2016), their ecological impact increases (
Baker and Clapham, 2004,
Ripple et al., 2014). The ability for these large predators to influence their prey through top-down forcing (
Baum and Worm, 2009,
Bowen, 1997) might become a significant concern for management agencies, especially considering commercial fisheries interests target the same species. In the GOA, some Pacific herring stocks have remained depressed long after commercial fishing stopped (
Rice et al., 2011). The hypothesis that predation by humpbacks might be impeding a rebound of herring makes sense for areas where humpback whale populations have significantly rebounded. Thus, linkages between humpback whales and fisheries in the GOA have frequently focused on direct competition for herring (
Boswell et al., 2016;
Heintz et al., 2010;
Liddle, 2015;
Teerlink, 2011)."
Can we over fish herring the answer is yes, Will the population recover the answer is sometimes...
