According to the CIA world factbook, Kuwait has 18,743 men reaching military age annually, and 737,292 men fit for military service between ages 15-49.
Prior to the first Gulf War, Kuwait had an army of about 16,000 men. After Gulf War I they were only about to reconstitute a force of about 8,000. Here's a description of the state of Kuwati army:
Unlike other Persian Gulf states, Kuwait has a conscription system that obligates young men to serve for two years beginning at the age of eighteen. Educational deferments are granted, and university graduates serve for only one year. In practice, exemptions are liberally granted, and most young Kuwaitis are able to avoid military duty. Estimates are that only 20 to 30 percent of the prewar military ranks were filled by Kuwaiti nationals. Military and security forces had been purged of Shia personnel during the 1980s. At the outbreak of the gulf war, Palestinians filled many technical positions, supported by thousands of Pakistanis, Indians, and Filipinos in maintenance and logistic functions. Officers on detail from Britain, Pakistan, Egypt, and Jordan provided military expertise. Lower ranks in the army and security forces were occupied predominantly by bidun who had taken reasonably well to military life but were poorly prepared to absorb training in operating and servicing modern equipment. In spite of reports that many bidun fought well against the Iraqis, many were expelled from the army in 1991 for alleged collaboration. Because of their removal and the removal of Palestinians and other non-Kuwaitis, the ranks of the services became seriously depleted. Few Kuwaitis volunteer for military service, and conscription is not regarded as an acceptable option. Under the circumstances, Kuwait will be hard pressed to meet its goal of a postwar armed strength of 30,000. A relaxation of the policy toward bidun was hinted at by the statement of the minister of defense that people of "unspecified nationality" may be retained after screening for loyalty and may even be given Kuwaiti citizenship. With respect to conscription, the minister of defense in July 1991 said that the system was being reviewed to make it more effective.
Seems to me that a war with Iraq, the Kuwaitis shouldn't object to conscriptions too much! Assuming 2 year draft with 80% "fit for service" ratio, that would give them a 30,000 men conscript force, plus professional soliders.