I was also under the impression that they were only allowing paid accelerations but over the holiday break, when there was less activity on the network, I was able to get 2 transactions accelerated.
It seems that they stop accepting new transactions once they reach a certain size of transactions waiting to be mined freely.
Of course, nothing has been mentioned on their website and I don't know the exact amount. I just know that it should happen very rarely. ViaBTC has around 10% of the total hash rate and it's estimated that they mine 1 block in every ~ 100 minutes on average.
This is quite interesting. I have noticed a few times that there are slots available at completely random times when you would expect them to already be taken. I guess they sometimes pause it for a while once they've reached a certain quota and restart it once they find a new block.