The short answer is no, you do not need to trade at work. You don’t want to be in a situation where you are in a meeting, on the road, or have frequent interruptions at your desk preventing you from making trades or position adjustments. Even worse, you don’t want to rush into a trade or adjustment because you know you are going to be “disconnected” for the next couple of hours. Trades need to be planned and well thought out. This starts the evening before or early in the morning before you start work.
Depending on the broker you use, you will have a variety of order types that will enable you to execute your trades while you are disconnected. I frequently use OCO (one-cancels-other) orders which can be bracketed around a trade and include the stop order and target exit order. If the stop or target order is executed, then the other order is automatically cancelled. I also use OTO orders (one-triggers-other) to enter positions and then submit a stop or target order after my position is established. Also, these orders can be day (cancelled at market close) orders or GTC (good-til-cancelled).
If your trades are properly planned before your work day begins, you can submit your orders before work and not have to worry about executing trades while you are trying to work.