Do I really need Exchange Server?
You don't need Exchange server at all. You can use SMTP service built into Windows Server to send or tap into an SMTP server that is already in use at the company (which may be needed in case of firewall restrictions on outgoing SMTP traffic).
I'd rethink the premise of the question. If all you do is send email then all you really need is the .net framework and an ISP with a mail relay. You don't need SMTP on the windows server at all for simply sending email. I'd instead suggest you think about what- if anything you could get for value if you had an excahnge server available for your app. For instance would a message tracking function (by sender not receipts) be valuable? Is there any archiving requirements? per sender handling functionality? Exchange (like many microsoft products) isn't just an application but a platform in its own right. The other thing to think about when working with the microsoft platforsm is that the value isn't in any one app but in the entirety of the stack from the client side on up. One of the ways to get instant value add for your application is to tap into the stack, rather than just create an app that solves problem X (Eg MyApp is the best solution for creating widgets and optionally integrates with exchange )