Hi Ray Dio,
Yes you can do that, but as semiconductors are the fastest FUSE out, it's better to put a diode across LED
when wired from a mains tranny, as Spikes on the mains, known to cause Switch mode supplies to blow up
can reverse volts breakdown the LED... whereas in a DC circuit, LED would be safe as houses

But running a LED from Half wave, is useful as any loose mains plugs etc, will show up easy, but not on DC
With any kit, that needs saving from damage from mains spikes, fit a so called "Surge Protection" 13 amp plug
with the VDR inside the plug, from either CPC Farnell or RS Components ect

Rod Watts