I don't have a definitive answer for you, but I'm pretty confident that the answer is -- No.
MATLAB is definitely not made available by default by Google Colab. (Dare I say, this is obvious, given that MATLAB is proprietary software, not open source.)
There is a very nice MATLAB integration for Jupyter, which implements the ability to launch a MATLAB kernel from a Jupyter notebook, but I'm as sure as I can be that that would only work locally, and that one cannot create a MATLAB kernel on Colab.
In principle, I can imagine that it is possible to install MATLAB on the Colab instance, but this seems very unlikely. I did not try.
If your code will run in Octave (an open-source MATLAB clone), then it seems you can run Octave on Colab, and that could work. But, it seems unlikely that a full-blown deep learning algorithm will work in Octave (especially if you are using functions from the Deep Learning Toolbox).
You could try MATLAB Online, which runs MATLAB in the cloud. The Deep Learning Toolbox is available there, but I'm guessing you don't really get a huge increase in resources available to you. (I haven't used it in a long time, but it was kinda slow and clunky when I did.)
Finally, you definitely can run MATLAB in the cloud (e.g. AWS or Azure). But, that will cost $, of course.
