AFAIK - no.
You should complete quest on any your 50 toon (and get free HK51 for this one character) and it unlocks possibility to buy HK51 companion for any other your legacy character for 1 mio. But there are two seperate types of HK51 companion - for Republic and for Empire. If you buy Empire HK51 for Republic char - you can't use it.
interesting. i don't think i would have thought to check for the correct faction. thanks for the info.