Yes, but it's not totally automatic.
Here is how I would do it.
First, import the image (above):
image = Import["C:\\Users\\arnoudb.WRI\\Downloads\\WqZ6swa.png"]
Next, with the image editing tools extract just the content area:
image2 = ImageTake[image, {18, 683}, {74, 1498}]
Then extract the "black" points:
pos = Position[ImageData[image2], {0., 0., 0.}];
Then get the data ranges (in the "image coordinate system"):
In[33]:= Max[pos[[All, 1]]]
Out[33]= 635
In[34]:= Min[pos[[All, 1]]]
Out[34]= 32
In[35]:= Max[pos[[All, 2]]]
Out[35]= 1425
In[36]:= Min[pos[[All, 2]]]
Out[36]= 1
Then rescale the data points and do a list plot (Edit: It looks like the original plot has some piecewise linear scaling or logarithmic scaling, which will make the correct transformation a bit harder):
ListPlot[{Rescale[#[[2]], {1, 1425}, {4000, 400}], Rescale[#[[1]], {635, 32}, {0, 100}]} & /@ pos]
Note how the data is "reversed" from the original image, since the original image has a very strange x-axis (it starts at 4000 and
then goes down to 400).
