In an ideal case, no. In a not-so-ideal case, one with the push access could theoretically replace any package on your system with a malicious version that you would pick up automatically using apt upgrade.

I'd trust PPAs more if they didn't have such broad possibility of misuse. For example, if I add a PPA that only contains package A, I should at least be warned if that PPA tries to install or upgrade package B. apt will only display that package B needs to be installed/upgraded, it won't inform me that it originated from that PPA.

I applaud elementary OS for not bundling software-properties-common by default (a package that allows you to run add-apt-repository). If you decide to install it, you should at least be forced to make an effort to open such possibility of misuse.