No. SMART designs are used to develop an optimized adaptive intervention. If your goal is to evaluate the effectiveness of an already developed adaptive intervention, then you should consider a confirmatory, randomized control trial (RCT). For example, in a standard 2-arm confirmatory RCT you could randomize half the participants to the adaptive intervention and the other half to a suitable control group (e.g., usual care).
Note that SMARTs are not an alternative to confirmatory RCT designs. The two types of trial designs serve different purposes.