Honestly this is a question all artists/designers face. There are methods that can take the fun or creativity out of a project but allow you to meet your deadline, as you put it.
Sound design is no different when it comes to this question. I feel like it's the end that justifies the means. OK so you used a drum from a drum pack you bought online but now your song sounds incredible. No one cares if you did or didn't use an original sound. I mean if you did and it sounded great, that's probably a hit song. Quality and originality fused together.
So if you want to spend 100+ hours doing everything explicitly from scratch, go right ahead, it's probably going to sound great and it might even boost your ego. The final word is that everyone feels that way at some point down the path of artistry and there's no way around it. It just means you're starting to see things your own way and maybe even have become a better artist for all those hours you put in.
"True art" is in the eye of the beholder and that is, once again, the finished product. Not the process.
Edit: Sometimes you WILL or WANT to use a pre-made sound. This gets into copyrights and legal matters. For example, clearing a sample of someone else's song before you use it in one of your own. Not sure you were asking about this specifically but it's worth looking into if you'd like to use other people's sounds. Sound packs that are bought usually let you use the sounds scott free though, im pretty sure. Creative Commons (CC) sound files sometimes have no stipulation as well. You just have to read into the details of what type of CC license the artist has implemented for that particular file which is usually somewhere around the same page you find it on.