Yes, AlertFirst will leave a message on an answering machine or voicemail. Our answering machine/voicemail detection listens for silence on the line before it begins to play your message. Sometime messages can be cut off though if there are more than a few seconds of silence at the beginning of a contact's answering machine/voicemail greeting, or if there's a long gap between a contact's voicemail greeting and a voicemail system prompt (such as after a contact's greeting, the voicemail system gives instructions to press 1 to re-record, 2 to listen, # to transfer to another line, etc.).
Answering machine/voicemail greetings that have a slightly long pause at the beginning of them in them will most likely trigger your message to play before the answering machine/voicemail greeting begins. Our recommendation would be to type or record your message twice so that contacts receive the full message in these situations. Additionally, live answer contacts will have the benefit of hearing the message again if needed (or they can hang up if they do not need to listen to the message again).