I wouldn't doubt it if they did gradually slow your heart rate down more and more at higher doses.
But that whole thing is an entirely new can of worms.
From my point of view, opiates increase blood pressure, increase respiratory depression(slow breathing rate) and induce bradycardia(slower heart rate). Whether or not they continue slowing your heart down at a gradual pace is a good question.
Finally, if you're trying to slow your heart rate down as a reaction to stimulant induced anxiety or tachycardia, take in mind opiates are not the best choice of tools to use for this.
If you wish to slow you heartrate, codeine and opiates in general are most certainly NOT the WTG! They are horribly addictive, and as Envy mentions abouve, also depress the breathing rate and everything else, esp. the bowels.... this is what really did for Elvis! I'd suggest you would be far better off going to see your GP, who will have a whole host of stuff that won't do you any harm, and will stop your anxiety about racing heart problems. Good luck...
Marathon running is one of those things I have never attempted, nor had any desire to indulge in - depite glowing reports of wonderful endorphine effects. If I can't take them in a pill, I'll just have to do without I'm afraid - couch for me every time!