I would think not.
The speeds quoted by Wi-Fi are often not what you'd think. I once read of a case where a speed referred to actual speed that the data being sent through the air, but ignored the overhead of the other required bits from the headers that protocols required. So, just because some data got sent at x mbps does not mean that sustained payload x mbps / second of payload could actually be achieved. Although there was some technical truth to the quoted specification, the speed did not mean what most people thought it meant, yet marketing was plenty happy to capitalize on people's beliefs.
I'm sure that N600 is faster than 54g, but that doesn't mean that you're going to get exactly twice N300. Especially with an extender, which needs to receive content, have some amount of overhead processing the communication, and then sending content.
When Wi-Fi was designed, the Carrier Select: Multiple Avoidance (CSMA) was designed to cause minimal collisions. This is because actual collisions (multiple devices talking at once) were tremendously expensive, requiring re-transmission. 802.11n MIMO may change that game somewhat, allowing collisions to benefit transmission. Still, after reading a book about wireless signals when I taught a college course on the subject, I became thoroughly convinced to not expect those numbers to be treatable in a sane fashion.
You're much, much, much better off using wired communication when possible. Wi-Fi is great for the physical freedom provided to mobile wireless devices. However, for any stationary objects, wired transmissions offer significantly lower overhead. There may be a benefit to a device like a wireless extender, such as easy installation for people who just want to read an E-Mail and really don't care about maximizing performance. If you're a person who actually cares about speed measurements enough to really care about numbers, investing in a wired connection between access points is the approach much more likely to yield pleasing results.