I am from India and am planning to get a new bicycle. In India the roadster bicycles are very common, hence are cheap and easy to get. Roadsters have 28.5'' diameter wheels. Is it possible to fit 700c wheels to roadster frame, install drops and new drivetrain (and brakes) to make it perform like a tourer?
I'm not sure of the exact size of your rims, as it doesn't appear that a 28.5 inch tire is mentioned anywhere in Sheldon Brown's rim sizing chart. However, there is mention of a 28 inch wheel which is used on "Indian Rod-brake roadsters". The actual measurement for this rim is 635 mm. 700c wheels have a 622mm BSD. This means that 700c road bike tires are smaller (assuming your bike has 700b tires mentioned on Sheldon's site). Which means you may be able to fit the 700c rims on your bike, provided your brakes have enough reach. Check the rim size by reading the numbers off the tires. There should be a number there like 635 or 700b if they do use the 28" tires.
As to the question installing drops and a new drive train and brakes, that might present other problems. If this is the type of roadster you are referring to, there's a couple things you'll have to look out for. Dropbars could be easily installed, but there's a lot of other stuff to consider. Is the rear hub spacing the right size to accommodate a wheel with a standard road cogset. Are there proper mounts for caliper brakes. The bike in the provided link has "rod brakes" that use rods instead of cables. Can the bottom bracket be replaced with one that is compatible with a crankset you like. It might just be easier to keep your eye out for a used road bike rather than try to convert a roadster into a road bike. You'll have to buy quite a few new parts, and often the price of the parts far exceeds the price of a bike.
I actually have done this with a flying pigeon. I put 700c rims on the bike and it worked fine. Im not sure its worth you investing the money based on one response, but I have definitely had good luck with it. It needs to be a single speed or an internal hub (that is what I did)
It's hard for us to speak with any certainty about your particular bike that's halfway around the earth. However, it doesn't sound like you'll be able to do it, 700c wheels are 29" in diameter and your wheels are 28.5" in diameter, so they may or may not be half an inch too big.