While taking appropriate precautions - yes.
First make sure that you are really on a busy.org site by checking address bar of your browser, it should start with https://busy.org
Then follow the link from the top right corner of a page. Make sure that's the link from busy site itself, i.e. not a link from someone's post.
Then you should be redirected to steemconnect. Again check your address bar. It should start from https://steemconnect.com.
It will ask you:
Do you want to authorize the Steem account @busy.app to use your posting role?
Important part is that it will ask you to authorize account busy.app (no other) and your posting role.
So it will in fact be authorized to use only posting-key operations, but you need your active key to confirm that you are allowing this.
Here you can see details about what exactly you are authorizing busy.app to perform on your behalf.
Thank you so much you have been so kind to a newbie like myself i will not forget your kindness.