PCB Reflow in oven, will solder melt before VRM's, caps etc get damaged?
Hmm... doing it in a domestic home oven is totally uncontrolled. It may also get you anally bruised from unexpected interactions with your domestic partner.

Reflow ovens for production boards typically use either radiant heat or what is effectively a giant heat gun. Heat is only applied over a controlled and timed temperature sequence profile and the boards are cooled quickly. I would be concerned you would need to have the board in the oven for far too long. Furthermore, reflow is done in a non-oxygen gas to prevent oxidation.

Some components probably wont mind too much, but others like electrolytic capacitors will boil off, and yes plastics can melt. 

Reflow Oven Types

Reflow Soldering

And it looks from your question that you effectively want to "touch-up" an existing soldered board. 

That is not what Reflow-Soldering means, and I would consider that a bad idea in general. 

A considerable amount of oxidation has accumulated on the joins and pins since the board was originally manufactured, and you have no way to add flux. There will also be considerable other contaminants, dust, and oils, that have accumulated on the board too. 

You are far more likely to find the solder balling up into beads and breaking connections than miraculously fixing some suspected loose connection.