Would Texas license plates still be valid elsewhere?

Yes. License plates are recognized across international borders by treaty, and the United States already belongs to the treaty that does it. A Texas plate would be honored when driving in the United States the same way a Mexican or Canadian plate is honored there now, and a Texas plate would carry around the world the way any country's plate does. You can already drive a foreign-plated car across a border. Independence does not change that.

Vehicle registration crosses borders by treaty, and the US is in it

Here is the mechanism. The United States is a party to the 1949 Geneva Convention on Road Traffic, under which signatory countries recognize one another's vehicle registrations. A car registered in one signatory country may be driven in the others, displaying its plate along with a distinguishing sign for its country of registration. That is the legal plumbing behind every foreign-plated car you have ever seen on an American road. An independent Texas would be part of the same kind of arrangement, so a Texas plate is recognized for driving in the United States, and US plates are recognized in Texas. Cross-border recognition of plates is not something anyone has to invent for Texas; it is an established treaty the United States already honors.

You already see foreign plates on American roads every day

Step back from the legalities and look around. Cars with Mexican and Canadian plates drive on US highways constantly, and US-plated cars drive in both neighboring countries. Nobody re-registers their vehicle to cross a border for a trip. A Texas plate would join that ordinary reality, recognized on the road the way every neighboring country's plates already are. The everyday proof that this works is parked in border-town lots and rolling down the Interstates right now.

Texas already runs vehicle registration at national scale

Texas does not need to build a registration system; it runs one of the largest in the world already. The state registers tens of millions of vehicles and issues their plates today, through an established Texas agency. As a nation, Texas keeps issuing Texas plates from the same capability it already operates. The design of the plate, the fees, and the rules are decisions for the future Texas government, the same as any sovereign country sets for itself. What is certain now is that Texas plainly has the capacity to register vehicles and issue recognized plates, because it does it every day.

Living in the US is a separate question from visiting

One honest distinction. Treaty recognition covers driving in another country, a trip, a visit, a drive across the line. Someone who actually moves to and resides in the United States long-term is generally expected to register and license locally, which is already true today for an American who moves between US states or for anyone who relocates between countries. That is a residency rule, not a barrier to a Texas plate being valid for travel. For the Texan driving into the United States and back, the plate is recognized; for the Texan who moves there for good, local registration is the same ordinary step it is for anyone who relocates anywhere.

The bottom line

A Texas plate stays valid for driving in the United States and abroad, recognized through the same road-traffic treaty the US already belongs to and relies on for the foreign-plated cars on its roads today. Texas already issues plates at national scale. Visiting is covered by treaty recognition; only actually moving abroad brings the ordinary step of registering locally, exactly as it does for anyone, anywhere.