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Answer: No.
Reasoning:
Stretching the rope by one meter per minute means that the snail, in terms of percentage of the rope's length, will remain in the same place. That is, in the first minute, it will crawl 1 cm, which is 1% of the length. The rope will stretch, 1% of the length will remain, but in the next minute, the snail will crawl half a percent... This results in an infinite series, like the one with Achilles and the tortoise. The snail is moving towards the end of the rope, but it will not reach it. Only after an infinite amount of time, yes, but that doesn't make sense.