Yes and no. There are ways and conditions to make them fully compatible so you can continue an older save, but you can also start again with a cheat-enabled QSP to be sure.
Edit:
Just for informational reference, in the QSP scope checking against a variable whose value is 0 vs checking against a non-existent variable is for all intents and purposes the same.
So, most new story triggers will work perfectly.
What won't work out-of-the-box non-zero initial values (like newly introduced characters) and stuff like arrays like it's used on the Characters Info panel, though you can also fix that kinda easily.