In short, no
Darkness must target...
a point you choose within range
... and a creature (your imp) is not a point.
note: this is only one ruling; your GM may rule that another creature can move the object, in which case you can give your imp the object you cast darkness on to carry (see the other answers on the linked question above)
There is mention of targeting a point on an object, so you might suppose you can target an object the imp is holding...
If the point you choose is on an object you are holding or one that isn't being worn or carried, the darkness emanates from the object and moves with it.
... but you have to be holding an object (or no one can hold it).
Once someone else picks up the object, the point is no longer on an...
object ... that isn't being worn or carried [by someone other than you]
... and the darkness ceases to emanate from the object.
note: the darkness will still be there, it just won't be tied to the object anymore, so moving the object no longer moves the darkness
Moving out of range
If you were to target a point or object (or if a GM overruled so you could target a creature), then moving far enough to be out of the spell's range would not end the spell. From the Spellcasting rules:
Once a spell is cast, its effects aren't limited by its range, unless the spell's description says otherwise.
There is no reason perceiving through your familiar's senses would explicitly restrict concentration. Only a few things can end Concentration (apart from willingly ending it):
Perhaps a GM might...
decide that certain environmental phenomena, such as a wave crashing over you while you're on a storm-tossed ship, require you to succeed on a DC 10 Constitution saving throw to maintain concentration on a spell.
And use the blinding of your own senses as an environmental phenomena, but that is GM-dependent.