There exists no accurate and official way to know the exact number of slots an org has received before the results are out.

However, you can look at the past year GSoC records of the organizations and gain a good idea of the number of slots they'll be getting this year. It's always in the ballpark range.

Also, if you have built an awesome rapport with the people in the org, you could actually ask them about how many slots have they requested from Google.

There's also a rule that Google penalises the orgs that failed their GSoC students and/or failed to submit their evaluations on time. This penalization could mean a reduced number of slots the next year. You can ask for these type of info from your mentors, if they are comfortable sharing that.