Absolutely. I don't recall that there are any Platform dependent calls in LabVIEW for Linux. Give it a shot, and please post here if you have any problems.
Congratulations for choosing Linux, and LabVIEW for Linux.
I have always been a proponent of platform independent programming, and of Linux/Unix (okay, ANYTHING but Windows...evil, pure evil...). If you develop in Linux, and run in Windows, you are in fact developing a platform independent program (at least, if there are NO platform dependent calls in your program...)
Good luck, and keep us posted.