If I make cantenna with overlapping pieces of metal sheeting, then how important is it to have electrical connection between pieces of metal?

If you mean a metal cantenna/waveguide assembled from several separate sheets or pieces, then yes—the electrical connection between the pieces is quite important, especially as frequency increases.

The reason is that the inside of the cantenna is acting as a conducting RF waveguide, not merely as a mechanical enclosure. RF currents flow along the inside metal surfaces. Ideally, adjoining pieces should behave electrically as though they were one continuous piece of metal.

For your radio-astronomy applications:

• 1420 MHz hydrogen line: good electrical contact is desirable, but the construction is fairly forgiving. Small gaps or imperfect seams are unlikely to ruin it.
• 6.668 GHz methanol: considerably more important. Poorly connected seams can leak RF, introduce loss, and disturb the waveguide modes.
• 22.235 GHz water maser: very important. The wavelength is only about 13.5 mm, so even quite small discontinuities become significant.

You don’t necessarily have to solder every seam. Bolted/riveted metal-to-metal joints can work very well, provided the surfaces actually make electrical contact. Bare aluminium touching bare aluminium with screws/rivets at reasonably close intervals is much better than two aluminium pieces separated by paint, adhesive, plastic tape, or a thick oxide layer.

If you’re thinking about using aluminium tape to join the pieces, there’s an important distinction: ordinary aluminium foil tape may have an adhesive that is electrically insulating. In that case the aluminium faces can look continuous while electrically being isolated across the seam. Conductive-adhesive aluminium or copper tape is preferable.

For a cantenna I would aim for something like:

        GOOD RF SEAM

   aluminium        aluminium
  ───────────┐    ┌───────────
             │____│
             ●    ●
          rivet/screw
       metal-to-metal contact

   RF current ───────────────►
        essentially continuous

For your 6.668 GHz methanol cantenna, I’d make electrical continuity between every metal section a design requirement. You can check it with your multimeter: from one section to the adjacent section you want essentially zero resistance (allowing for the resistance of the meter leads).