In short, yes. Pretty much every method of installation in Linux (except for maybe appimages and snaps) is bound to have dependency problems. However, the point of using apt to install .deb files is that it can still find dependencies. You can still have dependency problems with .deb files and apt, but they are not as common as installing them with
dpkg -i as your original post said (which is almost guaranteed to have dependency problems). In my opinion, your best bet is to just install it with apt and hope. :) apt will usually figure it out for you, especially with a popular package like Google Chrome, which is intended to be easily installed. Also, just to clarify, you do use apt to install from PPAs, just after you've added them to your source lists. So while you can run into dependency problems with .deb(s), you can just as easily do this with
apt install, even from the official repos.
In a comment, you stated you were more concerned about dependency problems caused by updates due to differences in versions of libraries. I moved my answer in the comments here, and added some stuff aswell:
This can happen, but again, there's not much more of a chance of this happening with .debs than with official repos. If packages are listed as conflicting with each other, apt will throw an error, no matter the source of the files. Packages can also list a range of versions for dependencies they work with. These can be viewed by apt or online at http://packages.ubuntu.com. I can't think of any with an upper range, but you can see this on a package like https://packages.ubuntu.com/focal/htop, which has several dependencies listed with minimum versions. Additionally, some libraries are integrated into the code at compile time, and thus not shared between packages. And a lot of libraries themselves have protections against this: backwards and forwards compatibility.