Just wondering if I can still have valid transactions without accepting incoming connections.
Example: I am working on a Windows-To-Go drive that has my Bitcoin Core on it. Sometimes I will be unable to open that port. Will I have any problems sending or receiving transactions?
No, you will not have any problems receiving, sending, or validating transactions.
The only difference is that all your connections willl be made by your node, from your node to others. There won't be any connections from others to you.
Enabling listening is a service you can choose to provide to the network, and clearly, some people need to enable it or nobody could make connections. But it doesn't affect your personal ability to interact with the network in other ways.
