Rick's answer concerns trying to combine the results of two (or more) DFT's coherently. I'm interpreting your question differently - does a single DFT provide coherent integration? If you are trying to detect a sinusoid then yes the DFT provides Coherent Integration. Consider a signal consisting of a complex sinusoid of amplitude 1 and zero mean white Gaussian Noise with a variance of 1. The input signal is given by
$$x(n) = \exp(j2\pi mn/N) +w(n),$$
where $w(n)$ is the noise and $m$ is an integer and therefore the frequency will correspond exactly with one of the basis vectors of the FFT or equivalently this means the frequency is exactly on one of the FFT frequency bins. Looking at the SNR of the input signal, the signal power is equal to 1 and the noise power is equal to 1 (by the given conditions). There for the SNR = 1.
Given the definition of the FFT as
$$X(k)= \sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N}$$
we can examine the resulting SNR in a single FFT bin. For the signal only case $X(k)=0$ except when $m=k$ then we have
$$ X(m)=\sum_{n=0}^{N-1}e^{j2\pi mn/N}e^{-j2\pi mn/N}=\sum_{n=0}^{N-1}1=N$$
then the signal power is $|(X(m))|^2=N^2$.
For the noise power in a FFT bin we use the expected value or variance i.e. then letting $W(k)$ denote the FFT of the noise only signal - then since W(k) is a linear combination of zero mean Gaussian variables then $W(k)$ is also a zero mean Gaussian variable and the variance is the sum of the individual variances in each term.
$$var[W(K)] = \sum_{n=0}^{N-1} var \left[w(n)e^{-j2\pi kn/N} \right] =var[w(n)] \sum_{n=0}^{N-1} |e^{-j2\pi kn/N}|^2= N \cdot var [w(n)] = N$$
where we have used the scaling properties of the variance and the fact that the noise is zero mean. The SNR in the FFT bin is $N^2/N=N$. This is the coherent gain of the FFT when the sinusoid lies exactly on an FFT bin. You can also view FFT as a bank of Matched Filters for a sinusoidal input and look at the theory of Matched Filters.
Note - the analysis can be generalized for any zero mean and independent noise process, since the scaling property still holds for the variance. It's just a bit quicker and easier to do for a Gaussian noise process.
In the case when the signal is not exactly on a FFT bin there is a processing loss, this is commonly referred to as Scalloping Loss. You can read more about this in the classic paper on Windows by Fred Harris.
Notice that if you average the magnitude of sequential FFTs there is no coherent gain, instead you are reducing the variance of the estimate caused by the noise. For white noise if you look at the magnitude of a single FFT then there is quite a variation across all the frequency bins. Once you start averaging the magnitude or magnitude squared then the amplitude will show reduced variation and will approach a constant value. This is referred to as non-coherent processing because by using the Amplitude you are losing the phase information required for coherent processing.