i would recommend it....
the thumb spica is used to assure that your thumb is immobilized and does not do any grasping or wringing actions, it is usually placed after steroid injection for your condition and specially so if the injection is a second treatment if the initial injection treatment failed to help.
proper placement or should i say "positioning" of the thumb spica is needed which i believe your doctor or specialist is well trained with. another alternative to the spica is a "simpler" dorsal hood splint which can be placed by an occupational therapist. if i remember right there should be some radial deviation and wrist extension of the affected hand/wrist.
pray this treatment helps, otherwise you might need to get surgery if symptoms persist or worsens.
lastly- make sure you ask questions to your doctor on what to do and expect for the next few weeks while on the spica ( therapy, icing vs heat etc etc ) .
heal well !