Yes thats possible.
To transmit 1 byte at 115kbps, it will take 75uS. So you got nearly 75uS between 2 bytes sent. You can utilize that time to do the processing like detect change on your parallel port, get the port value in variable and put it to transmit buffer.
Once you have initialized the serial port at 115kbps, even though you dont send bytes continuously, every byte sent will be transmitted at same data rate, but the total throughput will be less.
Go for higher frequency crystal. 89c52 supports upto 40MHz.