Yes, she can purchase the property w/o spouse.
However, there may be some problems. Texas is a community property state. Unless acquired by gift, devise, or decent, property acquired during marriage by either spouse is generally community property.
Community property is property, other than separate property, that is acquired by either spouse during marriage. All property is presumed to be community property unless it can be proven not to be by clear and convincing evidence.
The result is that the new residence will be community property owned by both her and spouse.
(The opinion above should not be taken as legal advice)