My simple answer is of course no.
A common reason women get eyelash extensions is to replace the job of the daily mascara ritual.
Do not apply it to the base because this will inhibit the growth of other lashes and causes shedding.
If you were to apply mascara to the entire length of the lash, this will result in increasing the weight of your lashes. And when the weight of your lashes increases, this weighs down lashes that are not fully matured, and causes damage.
So, if you absolutely must, then apply it to the very tips only.