Lot to think about when anchoring. Especially in a lightweight plastic boat. The term "tieing it off" would indicate it would be hard to "untie". That's dangerous. Investigate clam cleats or other quick release cleating system for quickly releasing your anchor. This now means you need a float on the end of your anchor line so you can come back around and retrieve it. Look around the site for other discussions on anchoring. It's awful easy to get in trouble when tied to something that just might allow the boat to be pulled under in a tide run, or get yourself wrapped around a piling. Whether you want the line out the stern or bow depends on where you're fishing and which way the kayak wants to lay. Anchor trolley type deal. See if that doesn't give you something to think about a while. Stay safe.
To answer your question, the side handle is strong enough to handle it. It's just not a good idea.
Tie the type of knot that releases immediately if you need it do just that.
You make a great point about being able to quick release. What's the best kind of knot to use to attach the anchor line to the trolley clip so that it can be released as quickly as possible?