it is possible but will give you far more work than what its intended for!
if you are keen to persue than.
on feature activated event you need to add the webpart from that section!
the problem is selecting what webapplication and keeping a recored of where its activated on!
so the simpler solution would be to create a feature that deploys a webpart. This webpart is the master webpart that holds records of other features and the webparts they hold. when you deploy a feature from the webpart it will add the webpart to the desigered location you select on the webpart!
do you get where im going with this? to clarify, you have a master feature that contains a master webpart, the master webpart is on a page. It has a list of features that you can activate.... click on the feature within the webpart and it will take you to another tab or somthing on the lines of that or using ajax it drops down to show where its currently deployed to (webapplication url, webpart name ect). also within this section you have a deploy button with a dropdown list, the dropdown list contains a list of all webapplication... select one and click deploy. once done it will add it to the list above of all deployed webapplications related to the feature.. to get the feature to deploy the webpart to the correct location you selected you need to pass that value onto the feature meaning you need to add that part into every feature you create!
its messy but the only way i think would be feasable!