Depends what kayak your in.
What are you using, Dag Midway?
Shouldn’t need a rudder, they look quite narrow and should be easy to steer without a rudder
If you’re paddling you can “lean” and use your paddle to turn or steer.
If you’re in a decent narrow yak like a Stealth etc not really, the rudder is more for tracking.
Having a rudder on my longer glass kayak was good for tracking but it can also cause one to become lazy and use it to steer.
Can be done I paddled often without rudder around there, and I know Cheater fished extensively around there for years with no rudder. Its strong wind that makes no rudder hard. Tide flow affects whole kayak evenly so does not affect steering too much. just have to do a bit of ferrying across tide to get where you are going ie point well upstream of where you want to go.
Danger of skinny kayaks if you are anchoring, and that really is an anchor and bait soak region, is tipping the boat when retrieving anchor...not a bad idea to be leashed to kayak in those situations