Well, I wouldn't say that you're crazy, just reaching a bit
From what I understand, and you've acknowledged it yourself in your post, beagles are VERY easily distracted by the scents of small animals. They were bred to hunt, so this isn't surprising. Of course, I'm sure that within the breed you'll find some beagles who are more interested in "hunting" than others (just like I have one working GSD and one couch potato GSD) but in general I would say no, beagles wouldn't be suited to serious search work.
Now, if you're just looking for something fun to do with your dog on weekends, then by all means go for it! But if you're looking to get heavily and seriously involved in real-life SAR work, I would choose a breed already proven to possess the qualities needed for such a task.
A beagle may have the physical ability to search, but the police officers and detectives aren't going to like it very much when he or she runs off in the middle of a search for a missing Boy Scout to chase a squirrel
I sure do get a kick out of the mental image though!

From what I understand, and you've acknowledged it yourself in your post, beagles are VERY easily distracted by the scents of small animals. They were bred to hunt, so this isn't surprising. Of course, I'm sure that within the breed you'll find some beagles who are more interested in "hunting" than others (just like I have one working GSD and one couch potato GSD) but in general I would say no, beagles wouldn't be suited to serious search work.
Now, if you're just looking for something fun to do with your dog on weekends, then by all means go for it! But if you're looking to get heavily and seriously involved in real-life SAR work, I would choose a breed already proven to possess the qualities needed for such a task.
A beagle may have the physical ability to search, but the police officers and detectives aren't going to like it very much when he or she runs off in the middle of a search for a missing Boy Scout to chase a squirrel

I sure do get a kick out of the mental image though!