Yes, an excellent tool Sivari! I do this quite a lot with lines that would otherwise descend below the range of the sax OR where it just sounds cool. The trick is in finding the right place to make the jump up or down. I haven't analyzed the interval jumps that sound best (although a 6th or octave seems common), but I can tell when it sounds 'right.' I suspect it's a combination of good rhythmic placement (usually the jump is on an upbeat) and an interval that sounds good.
Thanks for the examples.