This is something that can be done, yes. But I can't think of a time when a salesperson would want to do it. Best-case scenario, the timestamp will alert the prospect you left a voicemail at a late hour or on the weekend, and they'll wonder why. Worst-case scenario, they'll just think your desperate.
Conducting extra research on your prospects before you call them is always a good idea. This script from Mike Brooks is a great example of how you can use this additional information in your sales voicemails.

“Thank you for calling [company/person’s name]. We are currently unavailable, but if you leave your name, phone number, and message, we will get back to you as soon as possible.”
Increase the odds of getting a call back by mentally composing your message before each call. And remember, people hate it when callers state their name and phone number too quickly in voice mail messages – no one wants to listen to a message ten times to comprehend simple information. Begin by saying your name and company (if applicable). Then assume the person you’re calling doesn't have your number, so say your phone number twice. If your name is at all unusual, spell it the first time you say your phone number. Talk slowly like you were writing it down yourself. The second time you say your phone number, you can say it at your normal rate of speech. A gracious phone message is no longer than 30 – 45 seconds. Be pleasant, but also get right to the point. Keep your voice mail message to two points maximum. If you need to share more information, then say you will send an e-mail message with the rest of the details. Leave a specific message. There’s nothing more frustrating than a voice mail that says, “Hi, it’s me. Call when you can!” Even if you’re just calling to say “Hi”, tell them that in your message. End on a high note! You don’t necessarily need to say “Goodbye” at the end of a voice mail, because you didn’t really talk to anyone. Instead, try something like, “Look forward to talking* with you!”