In short, yes you should be able to get away with replacing your turtlebot's gyro with another similar one without having to "write a driver" per se--since most cheap gyros operate in the same manner: outputting an analog voltage proportional to the angular rate about the axis of the sensor package it should only require minor modification of the turtlebot's existing gyro.py python module.
A post on how to hook up a rate gyro mimicking the configuration in the turtlebot (its not specific to the ADXRS613 it refers to) can be found here. This can be useful if you don't actually have a turtlebot, but rather just a create with a laptop (no turtlebot power/gyro board).
Unfortunately the main distributor for the ADXRS613 breakout was Sparkfun and they've discontinued that breakout due to the chip being end-of-lifed by the manufacturer. You may be able to find some resellers that still have stock, but I haven't had much success.
UPDATE: There seem to be a few left here, however these will probably dry up soon.
UPDATE 2: It should be noted that ClearPath, one of the distributors of the Turtlebot has apparently switched to the ADXRS652 chip. Since they have in-house fab capability, its unlikely they'll produce a breakout for this chip--you'd have to make your own or wait for someone like Sparkfun to make one.
The MLX90609 breakout might make a suitable replacement (from Sparkfun or Active Robots). Again, if you're just operating with a iRobot Create then you can hook up the analog out of the gyro to the same DB-25 pins described in the first linked post. You may still have to modify
gyro.py in the src folder of the turtlebot_node package a bit. Taking a quick glance at that file shows a slightly different formula for calculating orientation than I'm familiar with, so here's the calculation (in C++) that I use on my cheap gyro (from bilibot repo):
double dt = current_time - last_time; // last time we read ADC
double maxValue = 1024; // using Create's 10-bit ADC
double vRef = 5; // 5v reference
double zeroRateV = avg * vRef / maxValue; // I calculate zeroRateV from a circular buffer during startup, avg is the average of these values
double sensitivity = 0.013; // mV/deg/sec from datasheet
rate = (gyro_adc * vRef / maxValue - zeroRateV) / sensitivity;
orientation += rate * dt;
You'll have to figure out from the datasheet what the sensitivity (mV/deg/sec) value is and substitute it in the equation above. It should be relatively trivial to modify gyro.py's publish method if need be to match the above calculation.