Again, the basic answer is probably “no”.
Let me compare it to something for you, as a lot of people wonder the same thing and ask similar questions…
If you bake a cake from scratch, beat the eggs, mix in all the ingredients, mix the batter, etc. Once the cake is baked, can you take out one of the eggs? It’s basically the same thing that you’re trying to accomplish.
Now, if the background noise was recorded in descrete stereo and the voice was recorded in mono and is panned center, the center channel extractor can help. You’ll find it in your effects menu. There are various presets, including “acapella”, which is the preset designed to remove the background and leave the vocal.
With serious time spent on careful EQ, you MIGHT be able to make the vocal appear a bit more upfront, but you’ll probably ruin the overall sound in the process. Still, you can tinker with the graphic or parametric EQ and see what happens!
Emmett