Would the ability to efficiently find Discrete Logs have any impact on the security of RSA?
There is a reduction from DL to RSA if the DL oracle accepts composite modulus. For prime modulus, a reduction is not known. I copied the following from this wikipedia page with minor edits. 

Let $n = p\,q$ be an RSA modulus. 


Generate random integer $a$ co-prime to $n$ and a random integer $x$ taken in an interval much larger than $n$, say $[1,1000n]$.
Compute $b = a^x \bmod n$ but don't tell $x$ to the 'discrete log oracle'. 
Instead ask it to find the discrete log of $b \bmod n$ (to base $a$). Let the value returned by the oracle be $y$. 
If $y$ is a solution, then so is $y\pm\varphi(n)$ where $\varphi$ is Euler's totient function, and $0&lt;\varphi(n)&lt;n$. It follows there are at least $1000$ solutions $y$ that lie in the interval of $1000\,n$ integers from which we picked $x$ uniformly at random, thus the oracle has probability $\le\frac1{1000}$ of finding $x$. There is thus a high probability that $y\neq x$. If so, $|x-y|$ will be a multiple of the order of $a$, which can easily be used to factor $n$. I will not go to the details of factoring once (a multiple of) the order of $a$ is known (since this is a well known method, also used in Shor's algorithm). If we are unlucky and $x=y$, then we start over.