Smoker!
The most probable answer is NO!
You won`t get Auto speed brakes with antiskid inop! To test this you can do the following experience on the classic 737s. You can`t do it on th 737NG since the Antiskid ARMED/OFF switch was removed. But if you fly a 737 classic, put the Antiskid switch off and then arm the speed brakes. You will get a Speed brake do not arm light!
WHY? Because the antiskid provides 60Kts wheel speed info for flight spoilers deflection! With Right strut compression the ground spoilers pop out! But since you had to acomplish the Speed brake do not arm checklist (witch says do not arm them and deploy them manually upon touchdown) you woun`t get also the ground spoilers!
However if it is only a partial antiskid failure, you may have auto speedbrakes, if the 60 Kts info is not afected!
But most cases you don`t
Cheers!
Happy landings
