It turns out that the answer is yes, which can be easily checked e.g. using this code
figure
xh = gca;
figure
yh = gca;
set([xh, yh], 'fontsize', 12, 'linewidth', 1);
Note that the 'linewidth' property of an axes applies to the lines that make up the axes, not to any lines plotted into it. If you want to change their properties, you have to either collect the handles of all the line objects, or search for line objects later using
lh = findobj(0, 'Type', 'line');
set(lh, 'linewidth', 1)
Here '0' refers to the root object, of which all figures are children.