It should be fine. For practical purposes modern NMEA 0183 is a plain RS232 without any handshaking, any standard claims otherwise notwithstanding.
I see that its minimal baud rate is 9600. Rather than using a baud converter (which seems one moving part too many), why not pick another adapter that supports 4800 baud natively? Google brings up this: Wireless Serial Port - Wireless RS232 - Wireless Serial Cable Replacement - Bluetooth RS232 - LM058 - LM158 - BTD-433 - BTD-430
BTW, how do you power it up? I didn't find anything about power requirements in the spec.