The problem with growing Asp. from produced seed is you have no control over which are males and which are females.

If you have the space and leave enough room to prune without disrupting roots of asp. planted nearby you can grow them.

People generally like to make sure they're getting male plants, but you seem to have a female plant there and not minding it. The males tend to produce faster with thicker stalks.

Oh yeah...you can always plant them in a "staging/sprouting" bed and move them after a year as transplants. You can select the best, prune male/females if desired, etc etc...

For consistency in germination you'd want to wait until spring to start seeds this way, though.