The (very) short answer is no, interpolation does not increase resolution: no new data, no new information (Note that strictly speaking, the usage of "resolution" is not appropriate according to common definitions of the term. Check also the comment of hotpaw2, and also his answer).
A longer answer needs the following spectrum visualization (time domain, continuous frequency domain, and discrete frequency domain from left to right). I assume no aliasing for the sake of simplicity and therefore clarity.
The interpolation technique preserves the information of the spectrum. The output of DFT is a set of frequency bins spanning from $-f_s$ to $+f_s$.
First, look at the continuous frequency domain, if you upsample your signal correctly, it is equivalent to increasing the sampling frequency. You wish to double the number of data, but it is just removing one-half the spectrum replicas of the sampling process.
Now, look at the discrete frequency domain. This version is normalized from $-f_s$ to $+f_s$ of the continuous frequency counterpart. As $f_s$ is doubled, the spectrum is then shrunk by a factor of $1/2$.
If we call $0 < \alpha < 1$ the proportion of non-zero frequencies before upsampling, it becomes $\alpha/2$ after upsampling. Before upsampling, DFT gives you $N$ bins for $\alpha$ then $N\alpha$ bins for the spectrum; after upsampling it is $2N$ for $\alpha/2$ then always $2N \times \alpha/2 = N\alpha$ bins for the same spectrum. No, your resolution does not change at all.
To have a "better" resolution, the only way is to add more data. In your example, instead of dividing to 30 frames, divide your audio file to 15 frames.