I doubt it, since there are significant protocol differences due to different feature sets; the 15 can do multi site (the 396 can't), GPS support for location based scanning, ect.
However there are solutions for having one software for both radios; both FreeScan and BCtool are freeware and support both receivers (FreeScan is, to me, a bit better since it supports many of the new firmware functions - BCTool, at least so far, doesn't). Scan Control and ProScan (commercial) will also work with both scanners.
See the 396 wiki article for links on these packages 73 Mike