Like the title says, I just want to verify if we have the need to install a secondary SQL instance on a server that already has one SQL Instance, will the installation of the secondary instance cause an outage on the first?
will the installation of the secondary instance cause an outage on the first?
I interpret your question as will running 2nd instance installation cause outage or affect services of already installed instance. If this is what you are asking then no, it will not but it would be advisable to run any new installation during non production hours. If you are asking about installation popping for restart then yes it may be as Fernando suggested.