No, the root of the problem that you are trying to find and cure would be divisibility. Your initial posting is full of "i dont know" and in that regard very valid. You fail to actually identify a problem yet want to make a connection mandatory, however long the duration might be. Bitcoins will be valued at supply and demand related rates. This is possible as long as divisibility is sufficient, hence the problem you are trying to cure is not there. You try to solve a problem that doesnt exist by introducing a system that gives alot of people with offline savings a maintenance overhead that is neither desireable workload wise nor smart in the pseudo anonymous context. But of course, you wouldnt know about that.
How will the market value bitcoins when the total number in circulation is unknown? Does it matter how deeply the bitcoins can be divided if no one knows if there are 10 million bitcoins in circulation or 20 million?
This is an honest question. Maybe someone with a better grasp of economics can tell me if it matters at all whether the total number of units of a currency that exists is known or not known; maybe it doesn't matter because people value the currency based on its current supply, by which I mean the availability of units of currency to purchase, not on the total number in circulation.
Like I said before I personally would find it satisfying to have a system where no units of currency could ever be lost and with Bitcoin we could have that; but practically speaking the difference between 0.5% deflation and 0.0% deflation is probably not very important on anything other than millenia time scales.