Spurious When $F_s/F$ is not an integer
As people who responded in DSPrelated to your question, I believe the fluctuation which are seen are MATLAB plot artifacts not a real envelope. Since you doubt if Fourier analysis could help us to see the spurious signal, I perform a more elaborate spectrum sensing method (MUSIC) to identify if there is other frequency contents in the signal through the code below:

s = 1200*10^6;%Sampling Frequency
T = 1/Fs; % Clock Period 
N = 2^12; % No. of samples
t = (0:N-1)*T; % Linear time interval 
F = 200.01*10^6; % Required Frequency
phase = 2*pi*F*t; % Consecutive Phase values in rad 
sig = sin(phase); % Time Domain Signal 
%% SPECTRUM ESTIMATION
X=corrmtx(sig,200,'mod');    % MUSIC SPECTRUM ESTIMATION
[W,P] = rootmusic(X,4);
f=Fs*W./(2*pi); %Frequencies 
unique(abs(f)) %Show Frequencies
P              %Power of those frequencies


if you check out the P for each frequency component, you'll see only the main frequency (here 200.01MHz) has non-zero value.