Technically yes, with VLC (View > Advanced Controls > Record). But the quality is low, and recording illegal streams is even riskier legally.
Astro is a paid subscription service. Official Astro subscriptions are tied to specific hardware (the decoder) or the official Astro GO application. Astro does typically issue M3u links to the general public for use in third-party apps like VLC or Kodi. Astro M3u Link