Will we get to know a successful detection immediately?

A single WU is not going to do that. The detection will be inferred from several of them, and thus from several clients in all likelihood. Some things that I hope I have correctly inferred about E@H/LIGO are as follows:
- the detectors ie. really big interferometers are a new venture.
- an opinion about the confidence of a detection is formed from examination of a 'signal' vs a 'background'.
- the signal is hopefully some astronomical event.
- the background are any other reasons for the interferometers to emit a value into the data pipe.
- a subset of the E@H crunching boxes will actually do the math on data obtained from time periods when gravity waves from sought events were actually flowing through the detectors.
- we still need, for comparison, the data when gravity waves from events of interest were not influencing the detectors.
- there is alot of work in the above. All of us volunteers are crucial to giving a confident answer to the science questions.
It is still cool to think that one's own box might contain a 'wiggle of spacetime'. I hope mine does! But in reality detections will be owned by us all.

That would happen according to the policy ( already in place ) of the LIGO collaboration. We at E@H are a very valuable component in the pipeline of analysis for that enterprise.

Try this link ( from the top right corner of the E@H homepage ), this also, and in particular this.
Also take some time to glance at the detector logs for Hanford and Livingstone. Enter username 'reader' with password 'readonly' to view. It will reveal the flavour of the sheer blizzard of factors to be considered in gaining the best possible data for our analysis here at E@H. The science teams are working real hard to yield that - which is the main reason we don't hear from them as frequently as some of us would prefer.
Cheers, Mike.