Yes, I may consider buying a second hand smartphone if it came with a 1 year warranty, and affordable.
Some work places require that their workers use either a Blackberry, and iPhone because workers need to use certain work apps which are only available on iPhone and Blackberry, or the app work best on a Blackberry or iPhone. Work places sometimes may only use Blackberry or iPhone for security reasons because they feel Android is not safe for work, or too hard to keep safe.
I think if you just plan to buy a Blackberry or iPhone to reply to work e-mail with a more secure e-mail app, reply to secure work messages/text and not plan to use it for mobile gaming, watching video, social networking, and personal use, an older second hand phone like the iPhone 5S or Blackberry Classic maybe good enough for your work needs without spending more money on a newer smartphone where some workers may not need a very fast phone to reply to messages, and video chat with their co-workers.