Will this fork increase the total number of bitcoins to be made?
No.
well, yes. Amount will exactly double - so value should halve at least. (formally one coin with one cap - then two coins with less cap combined as everyone with a brain will cash out before the madness occures)
I disagree. It isn't accurate to say that the total number of bitcoins will increase. Effectively one of the forks will be "bitcoin" and the other will be an altcoin. If that means that the total number of coins has increased, then every altcoin that has ever been created is an increase in total bitcoins.
A pair Gavincoin/Mpcoin for the direct warfare can be expected on some exchange. It'll be fun to watch but certainly nothing anyone wants to get caught up in. War could go on for months but eventually both coins become worthless in the end and will be replaced with altcoins.
Maybe people get good arbitrage opportuninty in case chaos isn't too omnipresent to even move coins on any of the two chains safely.
Probably 51% attacks from either side can be expected aswell as wild fluctuations not only in price but also in hash of both coin. It will be an epic act of cannibalism.
While this is one possible scenario, it is the most pessimistic, alarmist, and paranoid possibility.
It is also possible that the fork is implemented so well that the vast majority of users immediately accept it. There is no warfare. There is no arbitrage opportunity. There is no chaos. The widely accepted new code maintains and grows in value while the old protocol fades away into obscurity, abandoned to the purists and idealists that can't adapt.
It is also possible that supporters of the new fork vastly overestimate the support they have in the community. They try to push the change through clumsily and ineffectively. The vast majority of users immediately reject it. There is no warfare. There is no arbitrage opportunity. There is no chaos. The widely accepted old code maintains and grows in value while the new protocol fades away into obscurity, serving as a valuable lesson about the importance of consensus and overconfidence to its supporters.
There are an infinite number of possibilities in between those extremes.