If I understand your question correctly, the piece of information you're looking for is this:
If a word starts with a shva (which as you know, would be a shva na) followed by a bgdkpt (which would not have a dagesh because of the shva na), then if you add a prefixed particle, the shva will never become a shva nach, but only a shva merachef, and thus, there will never be a dagesh.
For example, if you have רְכֻשׁ, adding the ו you get still have וּרְכֻשׁ, and if you have מְבֹרָךְ, adding the ה you still have הַמְבֹרָךְ.
The only exception to this is the Qal infinitive with ל, which regularly adds a dagesh. For example, כְּתֹב and בִּכְתֹב, but לִכְתֹּב.
In short: Prefixes can never change the second letter of a word, with the one exception above.
שתה וגם גמליך אשקה