If Hope has vampire blood in her system but isn't a vampire; does it mean that if she grows old and dies she would become a vampire?
Hope doesn't have vampire blood in her system but a hybrid blood. To be more specific vampire/werewolf/witch tribrid blood. She is the only know tribrid till now, so we can't say anything for sure but speculate on the basis of what we know till now.
Hope while in womb, was able to make Hayley a hybrid during giving her birth and show more sign of hybrid nature then vampire one. Hybrid when killed don't come back as vampire, so I guess if hope dies she will not come back as vampire either. But what will happen if she drink vampire blood externally before getting killed is debatable, as her witch side will allow it but not sure about how her hybrid part will react. As when witches die with vampire blood in them they become vampires but hybrid don't.