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She'll be more than fine. It will actually improve your chances because she'll see you as an alpha who doesn't go out of his way to try to convince her, signalling that you have other options available.
If you take her to a restaurant with you paying, you signal that you are a desperate man ready to be exploited. This will make you less attractive in her eyes, and she'll think that she must not put out to not lose all the benefits that she gets from your courting her.

Demonstrations of wealth to impress the woman had their place in the old times, when a woman was selecting a man based even on his ability to provide for her. But today, a woman only wants a sexually intriguing alpha male.