I think I signed one once but it ended up costing me like $8 mil. I'd say as a general rule, don't draft those guys unless you're looking for a comp pick.
Also, definitely don't keep upping your offer, you'll be shooting yourself in the foot. You want to wait until they respond with a counter offer before you increase your offer. They will never accept an increased offer until they've sent over their counter offer, and if you keep going higher, their counter offer will keep getting higher too.