Are 6000+ troops assigned to border duty or not?
Yes...the article is quite clear in its explanation.
Many troops are on the border, looking for illegal crossers. Many troops are sitting in Border Patrol stations doing admin duties in order to free up BP agents to go to the border and look for illegal crossers.
AFAIC, boots is boots and bodies is bodies. The number of people deployed to the SW Border States has increased by more than 6,000 and the number of people actually on the border has increased.
That depends on the definition of "border duty."
The article states that "6,199 troops were somewhere in the four southwestern border states" and that the "Guard never intended to have 6,000 troops with their toes on the border."
There is no mention of how many Guardsmen are actually patrolling the border nor is there a number figure for how many Border Patrol agents have been (temporarily) freed up by the Guard's presence to patrol the border themselves.
The weasel-worded article goes on to say:
2,000 to 3,000 were on the border, most searching for illegal activity.
California has assigned more than 1,200 troops... half will be at the border looking for illegal activity; the other half will be in support roles ranging from plumbers to office workers.
Arizona - most of the troops are working at Border Patrol stations doing such jobs as communications and administrative support and vehicle repairs. Some are assigned to military bases to receive incoming troops.
New Mexico -- troops are helping spot illegal immigrants, building vehicle barriers and working in office positions.