"[is it] possible to use boxplot or a similar plotting technique to plot data that are not normally distributed? "
Yes.
Is it the best way to summarize a non-normal distribution? Probably not.
Below is a skewed distribution shown as a histogram and a boxplot. You can see the median value of the boxplot is accurate and the quartile markers (the edges of the 'box') show the skew. The outliers also indicate a skew. However, the median value doesn't indicate the expected value since the distribution isn't anywhere near normal. The histogram is much more descriptive and doesn't require knowing how to read a boxplot for the viewer to see the shape of the distribution or the expected value. But if you're more interested in the median and quartile values, a boxplot may better suit your needs.
x = pearsrnd(0,1,1,4,1000,1);
med = median(x);
clf()
s(1) = subplot(4,1,1:3);
histogram(x)
xline(med,'r-','Median', 'linewidth',2)
grid on
s(2) = subplot(4,1,4);
boxplot(x, 'Orientation','Horizontal')
grid on
linkaxes(s, 'x')
