on our caravan we have a goldsource df1765s regulator fitted and as far as I can see does nothing, When you turn if off everything still works the way it should.
Can I replace it with EBAY LINK. As I would like to have a batterty as back up power due to me needing it for a breathing machine.
You appear to have a regulated power supply fitted at the moment. This gives 12v 20amp output for mains input. I guess this has been fitted by a previous owner as a solution to provide 12v supply from mains only caravan which is how many older German caravans are equipped as standard.
So yes you can replace with transformer/charger as in your link which will allow you to fit a battery as well. I presume at moment though your caravan uses all 230v mains which is unusual as most caravans require 12v for lighting & taps, although some larger Tabberts etc come as 'dry' caravans with no plumbing.
For 'full' battery charging as well as running 12v stuff in the van without a battery, I might suggest you would be better off spending £70 on one of these...