I was wondering if it would be possible to purify Nitric Acid
Purifying it free of what contaminant?
by making crude Nitric Acid and adding copper to it, then collect the Nitrogen Dioxide gas and bubble it into a beaker of water.
Crude in what way? Too much water? Then no, dilute nitric might not release nitrogen dioxide. Paulings',
Chemistry is a good text book for understanding this. Also, nitrogen dioxide is difficult to collect, given that it attacks everything except maybe glass, and you will find it hard to make a concentrated acid this way.
Please let me know if this would work,
Its hard to know, because few people would bother. People who are qualified to handle it just buy it. People who aren't qualified to handle it just give up, hopefully before they hurt themselves.
and how much I would get out of it.
Now see, this isn't a question that can be answered at all. You get a certain percentage of what you start with whenever you manipulate anything. How much cake can you make? How far away is your destination from me? No one can answer those questions.