Can an Ackerman become a Titan Shifter?
Most probably not.

As you've mentioned by yourself, it was said that most Ackermans are immune to effects of titan powers, such as memory manipulation.

It is still not clear, what exactly was done with Ackermans, but apparently their bloodline is so modified, that they can't be considered as Eldians anymore. In one of the recent chapters (I'm not sure, 108 or 109), it was mentioned, that Survey Corps are not even sure if Mikasa can become titan at all, but it wasn't explicitly menioned, is that due to her being Ackerman or due to asian blood mix.