Not quite. Unless there is some sort of directed gravity pulse that ripples through the solar system (even then they are going to be less then a hand held gravity meter can measure)... The approaching gravity field will only increase as the black hole approaches... And that would be a gradual affair at first and would have a fairly uniform effect on the entire solar system as a single entity.
And since everything is falling at the same rate the atmosphere won't be falling any faster until the field strength is significantly different fromone side of the planet to the other.
Put it this way we don't personally conciously feel the change in gravity when the tide shifts. It would over a long time have an effect on our solar system... But the tearing off of our atmosphere would require a situation in which the entire solar system is falling in towards the black hole and be at a short distance in astronomy terms... The tides and probably the tectonic plates would show stress far earlier.
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