Just as Drunt Ba'adur has already stated, the Catalan Company would have needed much more in terms of manpower and probably technology. I have read some about them and as fas as I know, the Company was composed mostly of heavy infantry and some heavy shock cavalry. Their overall number was not large enough to lay siege to as big a city as Constantinople. Plus, I don't think they had any sophisticated siege weapons that they lugged around with them; their primary purpose as designated by the Byzantine emperor Andronicus II Palaeologus was to garrison certain cities and to augment the ailing Byzantine army of the time, which was devoid of any native heavy cavalry. They were recruited by Andronicus especially for their shock value against the encroaching Turks -- even the Turks were horrified at the Catalans' merciless brutality!
Some books you might check out:
John M. Sharp, ed. The Catalan Chronicle of Francisco de Moncada. Frances Hernandez, trans. El Paso: Texas Western Press, 1975.
Kenneth M. Setton. The Catalan Domination of Athens, 1311-1388. Medival Academy of America, no. 50. Cambridge, MA: Medival Academy of America, 1948.
Alfonso Lowe. The Catalan Vengeance. Boston: Routledge and K. Paul, 1972.
Angeliki E. Laiou. Constantinople and the Latins: The Foreign Policy of Andronicus II, 1282-1328. Cambridge, MA: Harvard University Press, 1972.