Yes!

Almost all the colonies advertised, trying to encourage people to join their endeavor (the exceptions being Rhode Island and the Puritans). This was mostly done through pamphlets that colonial projects would circulate throughout Europe, oftentimes with a targeted audience. There are loads of these pamphlets from the all over Europe, and they actually give us a lot of information about what life was like, not only in the colonies they advertised, but in Europe as well.

A notable example of a prolific advertiser was William Penn. He distributed several pamphlets, the earliest of which has the rather lengthy title: "Some account of the Province of Pennsilvania in America; Lately Granted under the Great Seal of England to William Penn, &c. Together with Priviledges and Powers necessary to the well-governing thereof. Made publick for the enformation of such as are or may be disposed to Transport themselves or Servants into those Parts." (sic)

It gives a tentative account of what it was like in the territory (tentative, since Penn had yet to actually go there himself), but mostly he tries to promote colonization itself. It addressed common apprehensions, and gave general information about the journey. His promotional material would often include some relevant details: the type of person they wanted, what would be needed for the voyage and for settlement, and how much it would cost. Some pamphlets also included a map.

Colonies needed people, and good promotion was a big part of convincing people to take on a long and risky journey to start a new life.

Source: Kane, Hope Frances. Notes on Early Pennsylvania Promotion Literature The Pennsylvania Magazine of History and Biography, Vol. 63, No. 2 (Apr., 1939), pp. 144-168

Right from the very beginning. More than anything else the early colonies needed people and money to purchase supplies. To that end tracts were written on both sides of the Atlantic encouraging people to emigrate or to supply financial resources.

Shortly after the Pilgrims arrived in Plymouth they sent back a document called Morts Relation. This document presented their arrival and trials in as positive a light as possible and was meant to drum up interest.

Even before them, still in the Old World, Richard Hakluyt wrote a treatise called "A discourse concerning Western Planting" to try and get support from the Queen of England for expeditions into Carolina. You can find a transcript here, warning PDF.