Brief Answer:
It would depend....

Detailed Answer:
upon where the increased protein is, and what protein it is.
Basically, I very much doubt you are referring to a spinal tap. Other than that the places where we test for protein are:
urine: Increased protein either means the kidney is NOT FILTERING OUT blood protein or DAMAGE is occurring
Not filtering out mostly is due to hypertension or kidney disease. Smoking won't help that, but probably is NOT the main cause. Hypertension, diabetes I see hourly as causes of this. over 10% of everyone I see has this.

Then there can be damage
There can be lupus, vessel irritation (which can be JUST from cigarettes but it's rare. It is called BUERGER's DISEASE), other autoimmune disease, drug or heavy metal injury. In damage, mostly you see blood with the protein, because the kidneys are just plain damaged. This can of course include trauma, or stones, or sickle cell--anything that just plain damages the kidney.

http://www.mayoclinic.org/diseases-conditions/buergers-disease/basics/definition/con-0000 (remember the U in it).

So, if it is kidney and Buerger's that's the answer, the smoking causes the vessels to blow up; stopping them fixes it. I doubt that is the case, here because it's really really rare. Also, mostly it causes inflammation of the kidney and people notice the bloody urine. Sometimes it's actually painful and bloody. You would almost certainly have A LOT OF PROBLEMS from it more than just a lab value of elevated protein, so, I really doubt this is what we're discussing.

SERUM/BLOOD protein Is due to entirely different reasons.
Ok, not entirely different reasons. Smoking irritates vessels and causes organ damage, small and slowly over time. This irritation process can cause an increase in inflammatory proteins. It can also cause some chronic low grade infection of the entire respiratory tract. The normal protein in the blood is albumin. The proteins elevated in abnormal processes are any of them EXCEPT the normal protein albumin. There can be an increase in the immune proteins (globulin) there can even be cancer of the cells that produce globulins in which case the globulin amoutn is SKY HIGH and it's not the normal infection fighting globulins but abnormal cancer globulin (one type, large amount, singular--globuLIN). If it's the globulins, you need to test that indeed it is all of them and not just one cancer globulin that is elevated...low grade bronchitis, not cancer. Yet.

Or it's just inflammatory proteins and not either globulins nor albumin. Happens. Bad because it's a marker of smoking induced overall inflammation but a chronic process causing problems over the entire lifespan and not anything that's just happened nor needing emergency treatment this month. To some extent EVERY smoker has some of this, so it IS occurring in your case, it may or may not be the only thing and may or may not have been the protein elevation of which we are discussing.

Or it's an elevated normal protein albumin. First, it is a NORMAL PROTEIN. There isn't a problem if it's elevated albumin. Changes of the blood concentration can elevate albumin slightly and temporarily (how much fluid you have, if you are slightly dehydrated and smoking can cause some minor dehydration, that proably is the reason). But the main thing is, if it's the normal protein, albumin, you don't have anything worse than a need to drink slightly more water.

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