Does changing the order in which CBSubs integration plugins are listed in the CB plugins list change the order of their execution?
Yes, load order will change the order of execution if the integrations are acting on the same trigger (most of them are).
When adding new users in the back end and assigning a CBSubs plan, I am using the SQL plugin to change the username from "_new_" to the user_id, and using the CBSubs email integration to send a welcome message. If I include the [USERNAME] placeholder in the welcome email, will it be replaced with _new_ or with the user_id?
Both use the same trigger so changing their order will change their execution order, but won't resolve your issue since the SQL action does not update the user object. You'd probably need to use CB Auto Actions and for your Email action under Parameters set Reload User to Enabled. You can use the below to perform various actions in CB Auto Actions based off subscription state.
Plan Active
Global
Triggers: onCPayUserStateChange
User: Automatic
Access: Everybody
Conditions
1: [var3] Equal To PLAN_ID_HERE
2: [var2] Equal To A
Plan Expired
Global
Triggers: onCPayUserStateChange
User: Automatic
Access: Everybody
Conditions
1: [var3] Equal To PLAN_ID_HERE
2: [var2] Not Equal To A