without looking at the schematic, it is likely all you would lose is the "reduced daytime running" light level...my guess which may or may not be a problem in terms of headlight longevity.
and now looking at the operation... the other "big problem" would be when and if you use your brights, both hi and low would be on at the same time since the HDM was "hot wired" to always be on.
Of course, the bigger problem would likely be that fact that the "hot wiring" would leave you with the headlight always ON... tough on batteries...