Yes, he can be arrested because when a probation violation is reported to the court the State's attorney files what is known as a motion to revoke probation. When that motion to revoke is filed a warrant for the individuals arrest is placed into the National Crime Index Center (NCIC) and that can be accessed to show a valid warrant through out the United States.
It would be better to go back to Washington and face the music rather than have to be extradited.
I would need some additional information; is the person on probation a juvenile (younger than 17 years of age) and did the juvenile’s parent(s) move to Fort Worth, Texas? Did the parent or the juvenile’s legal guardian make the Washington State authorities aware of the family’s move to Texas and seek permission of the Washington Court? What type of offense is the case related to, is it a felony, a misdemeanor, a sexual offense, etc.
Assuming the parent or legal guardian did not notify the Washington authorities of the move and moved without authorization this could be a very serious legal situation. I recommend you contact a criminal defense attorney in Texas and Washington - now. Potentially, the juvenile could be extradited back to Washington, assuming the Washington State authorities have issued a warrant for the juvenile. However, because the person is a juvenile there are special issues to consider under both states’ juvenile laws.