Does an R-Squared value indicate that there is sufficient data for a conclusion?
No. It only indicates a relative degree of "fit" of a data set to a particular curve.
The R-squared value is only one piece of data or evidence that may be used in deciding whether to make a particular decision. There is no definitive property of the value that can make that decision for you. It can be affected by the suitability of the "standard curve" to which the data are applied, the number of data points available, and the quality of the data itself.
In general practice any R-squared value of less than 0.5 would indicate that there really is no correlation between your data and the curve. A value greater than 0.8 may be construed as possibly indicating a significant correlation.
In all cases the R-squared value must include consideration of the error probability and confidence intervals for the data.