No. It takes a lot of skill to convince a Legilimens and avoid detection, but it is possible. Snape explains this to Harry at the start of their lessons:
βIt is true, however, that those who have mastered Legilimency are able, under certain conditions, to delve into the minds of their victims and to interpret their findings correctly. The Dark Lord, for instance, almost always knows when somebody is lying to him. Only those skilled at Occlumency are able to shut down those feelings and memories that contradict the lie, and so can utter falsehoods in his presence without detection.β
β Order of the Phoenix, chapter 24, Occlumency
Of course, Harry has never mastered Occlumency to this skill, but clearly Snape has. Otherwise, his role as a double agent would be rumbled the moment Voldemort used Legilimency on him.
I would guess that the skill required depends on the Legilimens in question. Clearly it takes exceptional skill to hoodwink Voldemort, but a less-skilled Legilimens may be easier to fool.