Yes, it's definitely possible. According to your camera, I'm not sure about the details, because you haven't provided the model. But I'm sure with it's driver came an utility (maybe a python script) which reads a picture (jpeg or mjpeg) and saves it as a file. Or it's also possible that the manufacturer has provided a developer documentation explaining the driver's interface, which you can use from your C code (probably involving reading data from a /dev/xxx file).
Now about the email part, you have several options:
1. most simplest one, use libcurl
2. if curl is too heavy for you, use an smtp-only library, like libquickmail
3. finally, if you really wanna go hardcore, create a mime-multipart string with your base64 encoded image, and talk smtp directly
on a socket connected to the tcp port 25 of a mail relay. Not very complicated, less than 100 SLoC, but you must read RFC5321
first. It's about saying "EHLO", "MAIL FROM", "RCPT TO", "DATA" commands, sending some header lines plus the mime string and terminating with a "." in a single line.