Can wider acceptance cause the value to fall? I've noticed lately that more vendors/companies are accepting Bitcoin: Microsoft being one of the latest and largest.

As far as I can tell, though, these companies seem to (mostly) immediately convert the currency into "real" money at the current exchange rate, and the transaction is often only completed once your Bitcoins are sold.

Again as far as I can tell (with my limited knowledge of economics), this will increase the Supply of BTC on the open market (more coins being sold) without particularly increasing the Demand (people without BTC are likely to just pay cash, rather than going through the hassle of buying BTC with cash to use with the vendor)

Does this mean that as more companies accept BTC, the value will drop?
The point you bring up is fundamental to understanding how the bitcoin market operates.

The majority of companies that have grown quickly in the space help merchants accept bitcoin. As you mentioned, these merchants generally end up selling bitcoin for fiat currency. Companies that provide bitcoin payment processing have grown more quickly over the past year than consumer wallet companies (which help consumers purchase bitcoin). Consequently, the bitcoin price has experienced downward price pressure over the past year, since we find more market participants selling bitcoin than buying it.

As regulation and banking becomes more attainable for bitcoin businesses over the coming year, we should see consumer wallet companies grow, which would lead to more people buying bitcoin. Until then, expect to see continued downward pressure on the bitcoin price.

PS: I'm the CEO of bitcoin exchange Coinsetter.