Can I use SPI for asynchronous serial input?
Quite simple no.  You do not have a clock to go with your RX data so the spi controller has nothing to clock the data with.  If you were to somehow manage to use a timer to fake the clock there will be drift possibly within a few characters, but eventually.  Nothing dictates that the sender is going as fast as they can, so there will be gaps.
The data coming in will immediately or eventually not be aligned in a desirable way, if possible you would still have to do your own search for start bits and stop bits and parity if used.  Slightly easier than bit banging but who knows.  Not sure if bit banging is the right term more like polling.
Crazy but you could create a timer that is 8 or 16 or some number times overclocked, feed that into your spi controller clock, strap the enable as enabled (does that part even have a dependent spi controller or is it master only), and then basically turn the spi controller into a logic analyzer from which you have to find the bit edges and extract the characters in software like a uart would.
You could also use interrupts if the gpio supports both edges or use two pins and tie the signal to both one to look for rising and one for falling, using a timer measure the time between edges and again have to in software do the uart decoding of the bistream.
Much easier to just by the right part with the right resources or get an external spi or i2c uart and hook that up to the MSP430, and let it do the uart work.  Maybe even a dual and have both uarts come in from there, maybe buy a lesser msp430 without a uart but with spi.