The simple answer to your question is "No" with a caveat.
The caveat is that there are signs that your network is never going to perform well. For example, the epoch accuracy fails to improve or even consistently declines over the first several epochs, or the validation accuracy is flat or declining. It could be that the validation loss starts high and just keeps increasing from the beginning. These are all bad signs.
Outside of this, however, it's very tough to know the model won't work well in the long run. For example, we have a model we built for solving a set of CAPTCHAs. The regression portions of that converged very quickly, but the portions that solved the rest of the CAPTCHA took something like 18 hours before they converged. Honestly, we only ran it that long because it was the end of the day and the regression piece looked so promising; there was nothing in the training behavior of the CAPTCHA solver that looked like it would work (even though our intuition was that it should.)
In the end, we have a 96%+ accuracy CAPTCHA solver that we likely would have killed if we had watched it train for more than 10 or 15 minutes.