An error message is always displayed: "Submissions are beyond limit. Please try later."
This is because the number of transactions that can be accelerated is very small ...
AFAIK there is a limit on how many transaction can be submitted per hour, so if you try to submit a transaction to them in a bad time you will recieve that message, maybe try to send again in xx:01 so your transaction will be accepted by them
That's what I have recommended in the past, catch their service as close to the top of the hour as possible. Every (or at least almost every) time I have done that, I got their "Acceleration succeeded" note. Then it was a few minutes to four hours until actual confirmation. I have about 10 transactions that worked with them, though I have not used the service for two - three weeks. So I don't know how it's working with about 82,000 unconfirmeds now.....
Still, a free service is a good thing. I salute ViaBTC for doing this, even if a gimmick.