My suggestion:
Instead of making the installation part of your TestExecute test project, run the installation seperately using PowerShell and then invoke your TestExecute test project. Unless you are actually TESTING the installation, it's not necessary to run it as part of TestExecute.
I am testing the installation of all the MSI's becasue part of my build steps are copying all the correct MSI's to a cloned VM, install it all (where my issue is now), then continue on with the testing of my application. I need this all to be automated so that is why I have it as part of my test steps.
The problem is this: as noted, there is probably something that TestExecute is using that your MSI needs to update. So, if you need to skip over that spot, then you will risk your application not being completely installed.
As for suspending the message... that's not a TestComplete/TestExecute question... that's a question for your developers to see if there is a command line switch or something that can be applied to the MSI to continue the installation. Or perhaps they can tell you what's in use.
TestComplete/TestExecute does include a method to RebootAndContinue (https://support.smartbear.com/testcomplete/docs/reference/program-objects/aqenvironment/rebootandcontinue.html) but I'm not sure that applies here. You need to be able to tell the MSI to ignore the prompt... You can either do that through some sort of UI check OR you need to pass it in as an MSI command switch.
In any case... good luck. Personally... this particular part of your test suite sounds like something where the ROI on automation is relatively minimal so, for me, I'd relegate that part of the testing to manual regression and continue the automation without it.
Probably you dont need it but I want to support @tristaanorge opinion.
To verfiy the installation you should use another tool. And do only the actual ui test with test complete.
