Yes, delaying the file load will negatively affect ReCAPTCHA's accuracy. From Google's docs on loading ReCAPTCHA:

Generally speaking, the more context that reCAPTCHA has about a page, the better informed it is to determine whether user actions are legitimate. This is particularly true when using versions of reCAPTCHA that don’t rely on user challenges. Thus, waiting to load reCAPTCHA until a specific restricted action occurs (for example, form submission) is generally not recommended.