Certainly possible, they need the cold, and the stomach acid, so yes, possible. The rounded leaves though do not look like blackberry.

The first sets of seedling leaves can look roundish. I have seedlings come up all the time just from dropped fruit.

I'm going to cover them (there are 3 seedlings there) up once they go dormant and let them grow next year. The seedling in the picture appears to be a thorny variety. It's exciting to see what kind of blackberry variety it becomes.

I would like to cross some in the future. I have to look at the genetics. I crossed some raspberries this fall. Prelude x Anne. I will grow out a few of the seeds this spring. I used Prelude as pollen receptor. I emasculated the flower before it opened. It took, so I have a good cross! Hey just for fun!
What the heck! What I want is a good tasting orange, see what happens. I used Anne because of the excellent taste. Prelude, as it seems to grow no matter what. Caroline would be another to consider, but I feel Prelude is more vigorous. Fall Gold might be a good yellow too, but at the time, the flowers were in sync so that was a factor too.
Once I move I can do many crosses and grow out many more plants. This is more for practicing crossing and germinating techniques.