Building a light rail service in that city would expect to have all the issues Newcastle had when they deployed.
The Newcastle Light Rail can not be used as a fair comparison to anything - it's a 2.7km line of frequent public transport (PT) on a peninsula in a 300+ square km sprawling city full of the worst public transport in the developed world of a city of it's population and size, services are infrequent (as low as once every 2 hours on some services), unreliable, lack morning/evening services, and passes major locations without stopping.
With that being said, things in Wollongong are a little different, services are poor, but not unusable compared to those in Newcastle, but would need improvement to make any light rail service get good patronage, mainly more frequent local services between Stanwell Park (at which point, might as well run all the way from Waterfall) and Port Kembla, and duplication and new local services and stations between Kiama and Wollongong (which would then speed up express trains as they would not need to stop at every stop.
If they are going to go to the effort to build the light rail though, it would have to go a greater distance than just the CBD to the beach and stadium to be worthwhile, a good option would be to run along the Port Kembla railway line, then through Warrawong and Shellharbour and connect back to the main line around Shellharbour Junction.
The thing with retail shopping is that people still spend that money, its just the location that varies.
Newcastle CBD is not the most central of locations, which is why it died. Forcing people to shop where its logically doesn't make sense is ridiculous. The LR may however help with redevelopment of the CBD encouraging more redevelopment increasing the residential population and this would likely drive more retail and other entertainment options in the area.
In the case of Newcastle, the places where people spend money are in locations which are too expensive for small business to operate as the rents in the suburban shopping centres are far too high and the streets are completely unfriendly to pedestrians and PT users meaning foot traffic is minimal.
At least Wollongong has the advantage of having a CBD that is actually central, and shopping, entertainment, health, beaches, education are all located pretty close to each other and to the existing Wollongong and North Wollongong railway stations.
Compare this to Newcastle where each of these faclities are located in a different suburb, often next to the existing railway lines, but with no stations and/or pedestrian access.
Even if the light rail in Newcastle does bring retail and other entertainment to the CBD, there is no way to actually get to said CBD without driving making the light rail useless, the main thing people talk about when talking about the Newcastle CBD is the lack of parking.
To add further insult to the Wollongong proposal, its a trackless proposal. I thought they already had a trackless option, called the bus network.
Seems like they are all trackless proposals these days;
-if it's going to run with traffic through the same traffic lights, on bus like frequencies, with no (or little) morning and evening services, then it's a bus, no matter what way they spin it.
-if it's going run in a dedicated lane through dedicated signals, on train like frequencies, with full morning and evening services, then the 'trackless tram' is not a bad idea to saves costs, but it's yet to be proven.
With everything being said, realistically, what are the chances of this councillor's desire to be fulfilled? current government policies see two catergories of populated areas when it comes to PT planning; capital city or country town, obviously capital cities need PT and country town can't justify it, meaning that non-capital cities like Newcastle and Wollongong often don't have sufficient PT with no plans to fix it.
Taking Newcastle for an example, it has an international airport, a 30,000 student university, a 30,000 seat stadium, and much more, but when it comes to the government and public transport, it's a country town.