Yes, to a degree. Much of early Portuguese and Spanish expansion was made possible through ties to Italian merchant houses. Colombus was only one of many Italian merchants operating in the Iberian peninsula. Similarly, many ships relied on crews drawn from various Mediterranean states/kingdoms.

It is also important to remember that during this time Italy was the victim, of sorts, of expansion by other kingdoms. Before the 16th c. Aragon had expanded in the western Mediterranean establishing an empire that included the Balearic islands, Sicily, Naples (most of southern Italy), Corsica, Sardinia.

In the sixteenth century, Italy suffered more invasions as France and a unified Spain (Castile and Aragon) fought over northern Italy. this limited major expansion by Italian states, but continued to draw mechants and private citizens into Spanish expansion.

Check out:

Shneidman The Rise of the Aragonese-Catalan Empire, 1200 - 1350

Lockhart and Schwartz Early Latin America has some good detail on Italian participation in expansion and conquest.

Mallet and Shaw The Italian Wars