Can I use a Y-harness to charge battery while in use?
This will "tend to work" in most cases.  

In some cases the load may be such as to cause the charger to undervoltage cutout or to go into a slow trickle up mode - but probably not if the battery voltage is kept withing usual operating range. 



Using that adaptor for its stated purpose would be risky.
Paralleling two high energy batteries could result in death of the adaptor, possibly one or both batteries and just possibly the connection maker if they were in different enough states of charge. 

If the price is in Singapore dollars it is very excessive. 

A suitably edited photo can be useful
A link would be a good idea.