I'm not convinced that plans for Carrie's new music will be, in any major sense, built around, or altered by, what Garth Brooks is doing. I think Garth and Carrie are likely to be seen today as predominantly different artists, appealing to predominantly different audiences. Significant parts of Carrie's audience have grown into Country Music at a time when Garth was absent. Since Garth's re-emergence, he has been largely a "Las Vegas" artist. This implies a "static" concert fixture, appealing mainly to an older, more affluent audience. Carrie's touring has been to a more immediate, "revolving" audience, spread among many cities, and appealing in large degree to today's radio audience. Garth's release is strongly tied up with his launch of a digital music store, which by his own admission, is intended as an alternative to i-Tunes. Carrie's album and single market is already used to existing outlets. The advance song that Garth posted did not suggest to me a likely mass appeal across Carrie's audience.
There's also the question of radio - where Carrie is the dominant female player. The idea that some fans hold that the "industry" is against Carrie is heavily coloured by the critical and award situation - but that is largely irrelevant to the release of her new music. The radio part of the "industry" plays Carrie significantly more than any other current female artist. There will be eager anticipation and readiness for new Carrie solo music. How radio treats the new Garth Brooks music is also largely irrelevant to that eagerness. Mainstream Radio currently treats female artists very badly - but, even so, it has to vary the mix, albeit to the limited extent that it allows, by playing some female participation - and Carrie is, and has been for some time, the top female radio choice in the format. She's been out of new play rotation for some time now - and much of radio will be almost as keen to get a new single as we are.