I suppose so, maybe GF put their name on a bracelet like that, although that bracelet is generically called an Expandro and was sold under the "Expandro" name and several brand names, including Kiefer-Cadman, Henry & Cie, etc. Most likely it's not branded by GF, but even if it is, it doesn't add much value. If you put it on eBay it wouldn't bring $50 IMO. So just value the watch without the bracelet.
The more desirable GF bracelets are generally the "original" bracelets they made for specific watch brands and models (Eterna, Zenith, etc.).