The short answer? No.
The long answer: No, copyright law requires you to have an appropriate licence from the copyright holders (usually the record label - not the artist - if they're in a record deal!)
There are three distinct rights for every piece of music:
- Phonogram copyright (the sound recording) (symbol: ℗, "P" in a circle)
- Composition, score, artwork, cover design, lyrics, which can all be included in one overarchiving copyright registration per musical work (symbol: ©, "C" in a circle)
- The Publishing right, considered separately by some
Each of these rights may be 'assigned' to a third party (e.g., a publisher or a record label) and this is what usually what happens when a track is released by a label. However you may be able to 'encourage' the artist to grant a licence for the music's use if the project is cool or they like it. Ultimately the person who has control of the sound recording copyright is the person to request a licence from.
You are in breach of copyright law if you use a copyrighted piece of music without a licence - moreso if you exploit that copyrighted composition for commercial gain (use it to represent the product or service, even if it's just background music). Whilst I think the current system of licensing music is crazy, that's just how it works for the time being.
Occasionally artists are willing to 'look the other way' if you agree a licence arrangement after the finished work using their copyrighted music is released -- this may not even be a cash payment, it may just be promotion with the band, song name and iTunes link at the bottom of the screen. However, arranging a license 'after the fact' still compromises you from a legal perspective, and you could be forced to stop using that music in your own work (and, worst case, be taken to court for copyright infringement) if the artist or label doesn't like it.
I concur with the other answerer's suggestion to seek Creative Commons licensed music; Jamendo is a good site to start on, and even if the initial license is CC-NC you can communicate with the artist to request a commercial use licence (or to be granted an exemption). You may also wish to try sites like YouLicense.com to seek appropriate sync licenses for music for a reasonable cost.