I'm afraid I am no expert and a quick look in the sources did not give a quick simple answer.
To begin with, it is important, I think, to define some terms which sometimes appear to be used interchangeably in the literature, resulting in some comparing of apples and oranges.
Pilots: does it include chaps actually flying airplanes or everyone with the qualification who might be employed elsewhere (such as air staff officers)? For example 20 Polish senior staff officers were attached to French air staffs.
Air crew/flying personnel: includes gunners, bomb-aimers, observers, navigators, radio-operators etc as well as pilots. To complicate matters, in Poland, the senior in an air crew would be the observer not the pilot (as was the UK practice, I believe). Thus air force officers did not necessarily hold pilot qualifications and some held dual qualifications.
Air force personnel: this includes everyone in the air force, from the commanding general down to the mechanics, airfield guards, meteorologists, lorry drivers, cooks and bottle washers. Pilots would have made up a relatively small proportion of the whole.
To answer your question, although I have been unable to locate specific stats, the figure of 1,600 pilots does not seem entirely impossible (especially if observer officers are included in this total). At its height, the PAF in France consisted of 1663 officers (including 4 female pilots), 6 officer cadets, 3265 NCOs and 3417 enlisted men for a total of 8351 (according to Kolinski). I wonder if the figure of 1600 pilots comes from an assumption that all the officers were pilots? Since some 9300 air force personnel had been evacuated to France and the UK from Poland in 1939/40 (specialists were prioritised), it seems unlikely that there were many untrained recruits needed or obtained from the Polish expat population of France.
Counting airframes in pre-war Poland as a guide to the number of pilots available is likely to lead you astray. For one thing, before the war, the air force was gearing up for major expansion and training personnel accordingly. 200 pilots partly-trained in Poland were in the process of completing their training in Marakesh alone in May 1940, and they were just the first batch. For another, you have the trained reserve and civilian pilot pool that can be drawn upon by the armed forces in times of war.
I am convinced that somewhere in my house a book on the PAF in France is lurking. If I find it, I may be able to provide you with a more definitive answer.