We have fostered (and currently do) and also have "failed" as fosters. I am also very blessed to have a number of good friends that foster, mostly because the majority of our friends are greyhound/pointy dog nuts like us.
A couple of points. By fostering, you are helping to provide the essential "bridge" between a life in racing and a new second life as a companion. This is an especially important task for greyhounds who don't have early lives that are anything like the lives of "pet" dogs in rescue. The help and training you provide will be of benefit for years to come, and will assist your lovely boy in making a smooth transition to his new life.
Contact after adoption - absolutely!! It's one of the nicest parts of fostering, seeing one of your charges doing well. Most greyhound owners are extremely social folk - your rescue will almost certainly organise things like regular walks, playdates, shows, picnics etc. Go along to them, and you'll probably meet up with your former boy.
One of my very dear friends who fosters for EGLR has now fostered approx 36 dogs. Every Christmas she does a wonderful newsletter to all us families who have adopted one of her fosters with news and updates. Out of all the families, only one hasn't kept in touch with her. I see her regularly and for instance she comes along to watch if I'm competing with Scuttlelurcher in a Rally trial nearby or similar. I regularly send her pics and we swop lots of news and info/pics on FB.
I know lot of people who maintain links with their foster families. For instance, foster family will have dog to stay during owner's holiday - that's very common, or dog sitting for a weekend away.
If you decide to adopt this gorgeous hound, that's completely understandable, but you should be very proud indeed of fostering - it's the foundation of so many successful adoptions. Yes, of course it's a bittersweet moment when you say goodbye to them (I've cried buckets after saying goodbye) but it's very much au revoir rather than Farewell.
As a lovely example, we fostered a beautiful greyhound many years ago. She went to the most wonderful home, and we kept in touch with her adopter, seeing them at events and having joint walks etc with our gang plus their two dogs (they'd adopted a second greyhound). Sadly, this owner experienced a period of very severe ill health requiring a lengthy hospital stay. Our previous foster and her new brother came to us for the duration so they could have a nice safe home environment, and avoid a long stay in kennels. We were able to visit owner in hospital and provide lots of lovely reassuring updates on the dogs. Sadly their health then deteriorated further and we were asked to keep the dogs as long term fosters (owner was too unwell to look after them). We provided a loving home for them (one has now passed away) and that original foster girl is still with us, snoozing peacefully on her bed nearby as I write this. We were able to (and still do) provide updates, photos etc for her original adopter - it's been a real comfort to them to know their dogs have had the best possible care. it's a great example of the long term relationships you can build between foster and adoptive homes, and why I always recommend rescues as life time back up really does mean just that.
Good luck!