That is the general idea - taking T4 orally raises FT4 and through conversion from T4 to T3 it should raise FT3 too. Sometimes the conversion is insufficient and one needs to take T3 in some form.
Well you should feel the full effect of this dose in 6-8 weeks. It's possible that this dose is not enough for you and sometimes one doesn't seem to feel any relief until one finds "the absolutely right dose", but it is entirely possible to feel some relief before you're "there".