The answer to this is pretty straightforward: yes, and yes, although probably less than you think because they were skilled practitioners who would have been able to both shape and use their axes in a way that would minimize that. As a note I am lifting this almost wholesale from Woodland in the Neolithic by Gordon Noble, who in turn bases his statements on a couple experimental archaeological projects, particularly the Draved Forest Experiment in Denmark.

The experiment really underlines the value of repeated practice and proper form--for example when the archaeologists first started they broke all of the axes they created within minutes. I am just going to quote from the book (page 51/2) because I think he writes in a very evocative way:

After this unpromising start, skills and knowledge regarding the axes and trees grew as the experimental work at Draved progressed. For example, TroelsSmith and his team soon found that body position needed to be altered from that used for a modern axe: only through embodied, practical use did an understanding of the technology emerge. The experimenters, along with the professional lumberjacks hired to work on the project, initially adopted the pose and techniques used with a steel axe, where the full upper body was involved in the axemotion, using slow, but high momentum swings, that involve the arms, shoulders, trunk, and legs, all participating in the swing. In contrast, with a stone axe, the team found that momentum had to be produced mainly through movement in the elbow, hand, and to a lesser extent the shoulder joints. The axe and the arms in this new pose described a trajectory of around 90˚ with the feet in a rigid position (Jørgensen 1985: figs. 21 and 22). The rhythm of cutting was of a much higher tempo than that used with a steel axe, and several hundred cuts had to be made to fell a larger diameter tree of 30–40 cm girth (Jørgensen 1985: 33; Steensberg 1957: 68). The techniques that the experimenters and modern lumberjacks developed were found to be similar to the few ethnographic accounts available of felling by stone axe (Jørgensen 1985: 30–1).

The upshot is that after they gained familiarity with the tools, a birch tree about half a meter in diameter could be felled in three and a half hours, and one fifth of a hectare could be cleared by one person in sixteen days. On the other hand, other experiments have shows that stone axes are ineffective at clearing trees bigger than a meter in diameter, and inefficient over about a third of a meter. For larger than that one can assume that techniques involving fire and girdling (striping the bark around a trees circumference, causing it to die) would be used. Other experiments point towards tool specialization: axes made of ground stones were not as sharp but easier to make and more durable than flint axes, so it could be that the former was used for the initial cuts while the latter could be used after the initial notches had been made.

For a bit of context, agriculture entered Europe almost entirely through migration--that is, by populations physically moving to a new land, not existing hunter gatherers adopting farming ways (foragers did eventually join with the agriculturalist population, but well after the expansion had occurred, there was a long period in which the two populations coexisted with intermingling). The two groups favored different territories as well: the foragers in the game rich marshes and wetlands, while the agriculturalists fanatically stuck to the areas of loess soil. The upshot of this is that the initial expansion of Neolithic farmers into northern Europe was indeed into "virgin" territory of dense woodland, as much as they may have tried to take advantage of natural clearings they had to do a great deal of the hard labor of felling and clearing themselves, they did not build on the efforts of previous generations. Despite that, the migration was quite rapid--the Linearbandkeramik (LBK) people spread from the Danube to the mouth of the Rhine in about 500 years. This rapidity quite thoroughly outpaced necessity, there really does seem to have been some sort of cultural value to movement and "founder's ethos".