Earlier this year DD with high VCI was diagnosed with both expressive language disorder and CAPD. Both came as a total surprise. (Started with a rule out CAPD eval and then audiologist discussed motor speech concerns with SLP colleague leading to speech eval. No one suspected expressive language disorder.) We did the evals at our state flagship university's speech and hearing clinic and insurance covered both - didn't even charge a co-pay. Other SLP's I spoke with would not accept insurance but would provide paperwork to be submitted to your insurance if needed. One would not accept insurance through her private practice but offered the option to have her students at the private university where she taught do the eval under her supervision and said that would be covered by insurance. So there is no one size fits all answer to insurance coverage. Unfortunately it may be a time consuming process to call all the various possible testers but could be worthwhile if you can get it covered.
