Yes, you can definitely do that, you can also ask it to monitor and send you notifications if anything happens, give you reports, increase limits over time, anything you need. You can also do the same via MCP from your own AI.
SMTasker runs in the cloud the scheduling but the actual automation is done on your phone, that is why it's safe/untraceable since it runs on your phone. For that reason you need to have a phone connected to a computer and that computer needs to be turned on, yes. You can simply let run on a secondary computer/phone and can access it from anywhere via the SMTasker online dashboard or via MCP from your AI.