Your front shifting performance will likely decline, as the front pins and ramps will no longer be properly aligned to pick up the chain, but 52/34 will not be the Chain Ring of Death. Assuming this is more touring than racing, you are probably not having to shift under load, so this may not be a major problem. Also, in the Dolomites, you are probably in the big ring, or in the small ring, and not changing between them all that often.
A small ring and a chain keeper are probably a much cheaper solution than a full compact setup.