This can go one of three ways.
Good: SO is a success, Shenmue series gains a ton of new people in the community. Sega (or whomever is in charge) makes a ton of money and gives Yu the go ahead on Shenmue III.
Bad: SO is a moderate success. Some people leave the community, some new people join. Sega (or whomever is in charge) makes about at much as they are spending to develop the game/maintain the servers and Shenmue III is still a possibility, as it is now.
Ugly: SO is a failure, many current fans of Shenmue give up on the game due to some a bad release and very few people join the community. Sega (or whomever is in charge) does not profit from the game and Shenmue III has a worse chance of being made then it did.
It's up to whomever is in charge now to make this game quality. If it sucks, then I doubt Shenmue III will be made. If it's good and whomever in charge profits greatly, then I can guarentee you that Shenmue III will begin production. Sega (or whomever is in charge) needs to really work hard and make this game as good as humanly possible, continually update it so it maintains a good player base and ADVERTISE. Get people into Shenmue so they will buy this game and probably Shenmue III!
Personally, I will probably buy this game even if it sucks because I think real time Shenmue fighting would kick ass online.
No one knows anything right now, we hardly even have any idea what the game looks like nonetheless how it plays and its quality. Give it some time, read articles and look at pics so you can give some kind of educated opinion before claiming "IM NOT BUYING THIS, SEGA SUCKS!!".
P.S: I highly doubt 'Ugly' will happen, 'Bad' seems likely but if Sega (or whomever is in charge) does a damn good job and gets Shenmue Online's name out there so people buy it, I suspect a 'Good' is possible.