Affirm. You can get your CFII before CFI. A lot of the factory schools do this - in fact, one school does CFII, MEI and then CFI. The reason - you do the CFII in a C-172 or some other simple trainer, then you go do all the complex manuevers in the twin and then the CFI ride is back to a "simple" airplane since you have already demonstrated the "complex" stuff in the twin. The other reason is that the oral for your "first" ticket gets to be more "instrument" based and the questions on the airplane are only on a "simple" aircraft - remember your "first" CFI check ride is with an FAA person or one of the FAA designated DE's. All the add-on's are with a DE of "your" choice.
If you think about it, there is a slight cost saving in doing it this way and you are doing less switching back and forth between simple, complex and twin aircraft.
And for all those still scratching heads, look at the PTS for any Instructor rating - there is a chart which show "Required Area of Operation" that can be waived if the candidate already owns a certificate.
If you intend to get "all" your ratings and then teach - pick the simplest and most cost efficient way. If you have the need to teach - then get the CFI (ASE) rating first.