Our church would allow you to have the Lord's Supper if you were still a member in good standing at your other church. I imagine if you weren't a member anywhere for a really good reason (your church doesn't have membership or the distance thing, maybe), but met with the session, you could still participate, since I think the only reason they insist you are a member in good standing is as an easier way to fence the table than interview every person.
We were not members of our church for over a year and we still could participate in Lord's Supper and could take part in various ministries, like nursery duty or church work days. We were also welcome to the small group meetings, etc.
We were Presbyterians, and they knew that, and we were still accountable to our old church, but I don't think there'd be a difference between types of non-members, if both believers.