Unfortunately the answer is no. It depends on damages, the adjuster, the particular insurance company, the amount of coverage, cooperation of the insured, and on and on. In Texas, the insurance company for the person that hit you has no obligation to treat you fairly or for that matter timely. I've seen to many times where the insurance company intentionally delays hoping you give up. Good luck and sorry to hear about the wreck.
Mr. Horowitz' response is "spot on." If your only damages are the car and no one was injured (no Bodily Injury claims) then it is usually a much faster track. Some good insurance companies can get you down the road in a few weeks, others will stall and take months. You may also have the option of making the claim on your own comprehensive insurance policy and then your insurance company will get restitution from the defendant's insurance company. This is usually much quicker.
Good luck and Godspeed!
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There is no real timetable for the process to take. There are time limits for the insurance company to respond, but no real time limit to finalize the process. In fact, some insurance companies try to draw things out as long as possible if you have no attorney. They hope that you will give up or miss the Statute of Limitations to file your lawsuit.
If you are concerned, it is time to hire an attorney.