That's kind of a strange way to do things, but here's something that might help.
Suppose you have a route like so:
map.connect ':controller/:action/:id'
Then /people/edit/1?gender=male would route to the edit action on the people controller, and params[:id] would be 1 and params[:gender] would be "male".
So to answer your specific question, as far as I know, no, you can't do that. But to do what you're saying wouldn't be very RESTful, if you care about that, and any functionality you need could be done more easily with other routes.
For example, you could have a q and a search action in your controller. With the route above, your examples would be /people/q/hello and /people/search/hello.
Or you could have a route like this:
map.connect ':controller/:action'
And then /people/index?q=hello and /people/index?search=hello could be filtered in the code by an if statement for params[].
To reiterate: No (as far as I know) but you shouldn't want to do that anyway.