That will allow you to request information from the ESP8266 but the rate you can request said data may be limited. It almost sounds like you want to stream data using the ESP8266. If the request method does not work you can google "esp8266 stream data" and find a few existing projects doing just that.
The part I currently see that will make all of this hard is the MAC side of things. Are you writing a program for it to read and convert the data automatically? If you are writing your own software on the MAC you could use the stock AT firmware on the ESP8266 connected to the sensor without the Arduino. Then your MAC program could use the AT commands to manipulate the pins and get the data from the heartrate sensor. But at that point you would have to basically write a library for the MAC to read the Heartrate monitor.
I have only used the ESP8266 as a web server and set up the AT firmware to run it.