Connecting tablet to VGA projector
Yes, it's possible. Some devices even have an official (branded) adaptor for doing this, such as the Asus Transformer TF-101. As you surmise, though, if the tablet doesn't support it, external convertors are quite unwieldy and typically need their own power supply, as they typically have to buffer a whole frame at a time in order to work.

Newer data projectors support HDMI or even MHL input, which allows you to use any tablet or phone with micro-HDMI or MHL output, with the appropriate cable.

Using either method, the presentations don't have to be of what is on your screen. Android 4.1 and up provide a way for apps to send different visuals to the external display from the built-in screen, so (for example) presentation apps can show your slide on the big screen and notes and controls on the tablet itself.