English Silver Spoons by Michael Snodin suggests that the catch phrase and spoons occured slightly earlier than 1776, closer to 1770; this is supported in Spoons 1650-1930 by Simon Moore who dates one of these spoons to c.1770. I'm not sure why antiquesilverspoons.com dates them as circa 1776, when "circa" is usually used with dates ending in 0 or 5. Either they know something the spoon books don't, or they're trying to give greater credibility to their dating.
Even taking this earlier date into account, your theory still sounds very possible, but more likely the growing unhappiness with English rule over America simply added to the feelings of inhibition of the time rather than resulted in this design by itself.
I think the word liberty has been used far to widely and frequently as to be able to accurately assign this particular use to that of American colonists.
You'll have to excuse my ignorance of American flatware, but were there any political designs on spoons your side of the Atlantic; perhaps, like you theorized, against British rule.