No. Although there may be some improvement, HIT isn't designed to improve upon cardiovascular fitness in any way, shape or form.
HIT (High Intensity Training), as popularised by Arthur Jones in the 1970's, is designed to improve strength and muscular hypertrophy by performing weighted exercises, usually on machines (such as the Nautilus ones created by Jones) for one set to absolute failure, followed by a prolonged period of rest to allow those muscles to recover. My understanding is prolonged can mean anywhere up to a week of rest.
As cbll explained in his answer HIIT (High Intensity Interval Training) would be an idea way to train up for sparring in pretty much any martial art.
Given your limited equipment, you could perform HIIT with some bodyweight exercises (hindu squats could work), sprints, rope jumping (skipping ropes are pretty cheap and you don't need much room) or, if appropriate, just work a heavy bag. If you have access to them, kettlebell swings are pretty good as well.
The idea is to get to the point where your training either matches or exceeds your sparring, though probably with standard interval training, not high intensity interval training (so, if you spar for 4, 3 minute rounds with 30 seconds rest between rounds, then build up to the same with something like rope jumping).