To begin with, we must understand that the 10-hour paralysis is a homebrewed effect, and such a condition was decisively not in view when the rules for resting were written, but we can try to surmise the interaction between the written rules and this homebrewed effect.
On the surface, the rules for long rests make no mention of the paralyzed or incapacitated conditions. So in the strictest RAW sense, there isn’t a reason why you wouldn’t benefit from a long rest.
But we can make some inferences from the description of long rests to rule the other way:
If the rest is interrupted by a period of strenuous activity — at least 1 hour of walking, fighting, casting spells, or similar adventuring activity — the characters must begin the rest again to gain any benefit from it.
I would argue that suffering from a particularly potent paralysis poison for ten hours is going to fall somewhere in this category of “strenuous activity”, but maybe that depends on how your DM wants the poison to paralyze you. Do you simply lose nerve function in your body and can’t move, or does the poison violently lock up your muscles?
To determine if this paralysis falls under strenuous activity, you would have to ask the one who invented it.