No, there were no Gantt charts, but that's not to say there wasn't similar tracking of information, time spent on certain elements, materials, etc

The design/building team for major medieval projects was actually fairly complex.

At the top you would have the patron who has requested the building. Often these were ecclesiastics (bishops or abbots) or the noble who had commissioned the building. We see these figures all the time with regards to their buildings. Fulbert (1006-1028) for the Romanesque work at Chartres, Roger, Bishop of Salisbury (1102-1139), Bernward, bishop of Hildesheim at St Michael at Hildesheim (1010-33), and Gundulf, bishop of Rochester, who worked on the Tower of London (1078-87). We also know that monks on a regular basis participated in the physical work of the construction, the Cisterians were particularly prevalent because of their emphasis on manual labour. We also have evidence that Edward I (1272-1307) wrote to his masons on the requirements of his castles requesting certain features and orientations.

Beneath the patrons there was some level of organization, design, and construction. Typically, and I use typically loosely here because our documentary sources are few and are at times difficult to discern specifics, the works would be administered by a clerk, sometimes with building knowledge, but not always. We have evidence for this is incriptions, one at Chadenac

Here lies William the Poitevin, clerk of William, builder but not carver

It was clearly important to point out that he was not in charge of the sculpture, but the overall building. As building became more complex, it became more necessary for planning and experienced masons. Romanesque architecture can become very technical with the fitting together of sculpted archivolts, as an example, which would require a more experienced mason and not a clerk. As a result we get the emergence of master masons in the late 11th and early 12th centuries. William of Sens and James of St. George are two examples. They were responsible for tasks like stone procurement, working out the dimensions of the works, laying out the plan on the ground, creating templates for the masons, and managing the building systems including pulleys and scaffolding. The accounts of Gervase on the rebuilding of the choir of Canterbury Cathedral after the fire in 1174 makes it clear that William of Sense was in charge of the works, not a patron or clerk (until he fell from the scaffolding and died). There would then be other craftsmen such as master carpenters, etc. It wouldn't be uncommon in the 13th or 14th century to have the patron, clerk, master mason, and master carpenters all working together on a building project, and not necessarily a single one of each, but multiple master masons, clerks, etc. These were absolutely massive undertakings in terms of resources and time.

Back to Gantt charts, still not being used, but the projects didn't just get built willy-nilly. It was quite common for medieval buildings to be built section by section, starting in the east and ending in the west. Alternatively, it was common to renovate buildings and dismantle them only section by section to rebuild the same way. This would of course require time frames, plans, and coordination. For example, the procurement of stone and materials was a major issue at times. We have several accounts of abbots and churchmen wandering forests looking for appropriate sized trees and quarries. In the case of William of Sense, he sent templates to the quarry at Caen where carving was undertaken, which again would require coordination and record keeping (hello Clerk). So in a way there were project managers and foremen. The last question, would the average mason have had an idea of the finished product? I'm not aware of any sources on this, but I will say this: if I'm hiring you to build something am I going to tell you to go over there and start sticking stones together or am I going to tell you to go over there and start sticking stones together so that we can build the tower. Assuming you have the appropriate skills I could lay out the plan on the ground and say I want this 10 feet high and you would be able to do it, so yes they probably had a good idea of what they were doing.