The D820 is a North American model utilizing LTE: Bands: 1/2/4/5/17/19/25/26/41.
Globe uses Band 3 and unfortunately that model;s LTE capability would not work in Globe's network.
(It should work in the rival network which utilizes Bands 1,3 and 5)
It was mentioned here
that LTE Band 41 under Globe, so Nexus 5 D820 will work on that band.
However, it seems recent (Sept 2014), so not sure if it has been setup already, on limited areas, and needs time to make it widespread.
As far as I know Globe still uses LTE Band 3 using 1800Mhz frequency, as for the list in Wikipedia this is still in the works and currently being deployed in the Visayas and Mindanao region as of the moment.