No, it won't work on the Spark Core. Been there, done that. The AM2315 shares the same peculiar timing requirements as the AM2321 and like. If you take a deep dive into Section 7.2.4 I2C Communication Timing in the AdaFruit manual, you will find that the Spark Core Wire firmware will not be sufficient to meet the AM2315 requirements.
I have then followed the manufacturer's example and wrote a library for this. It was originally for the AM2321 but it should also work with the AM2315. You could give it a try and let me know if it works on your device. Note that I have hardcoded it to use D2 and D3 for the custom I2C and I don't think my code would allow you to share with other I2C devices on the Spark Core.