Can I program a MSP430553 IC using the TIVA C development board?
The TIVA C is an entirely different architecture from the MSP430, and as such it's programmer cannot be used to program an MSP430. 

TI has a nice list of all official MSP430 Flash Emulation Tools (aka programmers+debuggers) on pg. 11 of their MSP430 Hardware tools user's guide. It shows very explicitly which launchpads and FETs support certain MSP430s. I highly recommend using this table to decide on your purchase.

If you don't care too much about whether the programmer is "official", a nice alternative is the GoodFET, though it seems to be a little less plug and play.