If I exhaust my Unemployment Insurance benefits and remain without a job am I still counted as unemployed in unemployment statistics?

Yes, anyone who is without a job but available to work and was actively looking for work sometime during the four week period ending with the reference week (week including the 12th) is counted as unemployed. The total number of unemployed is not based only on the number of people collecting UI benefits. Unemployed persons who are not collecting UI benefits are included in the results of a monthly household survey known as the Current Population Survey.