Yes, you can use same mobile number to register on multiple devices. Your profile along with downloaded songs, purchased songs, liked songs, playlists and subscription will synchronise across devices.
But you will still have to re-download songs in memory.
Steps to re-download downloaded songs are mentioned below:
Step 1: Launch Wynk Music
Step 2: Go to My Music
Step 3: Go to All Downloaded
Step 4: Tap on 'Download All' button
Steps to re-download purchased songs are mentioned below:
Step 1: Launch Wynk Music
Step 2: Go to My Music
Step 3: Go to All Purchased
Step 4: Tap on 'Download All' button
Please note that downloading all songs may take time depending on number of songs to download and network conditions.