I'm not an economist, but…

No, that's very unlikely.
Starting from your assumption that the network splits into two persisting blockchains^*:

• The number of active participants of each network is reduced. This reduces the utility of the network. → Negative effect on the value.
• The amount of transactions that can be sent increases. This improves the utility of the network. → Positive effect on the value.
• The shortterm security of both chains is reduced as hash power is spread to two chains. → Negative effect on the value.
• The longterm security of both networks is reduced, as one or both of them become more likely to cease existing. → Negative effect on the value.
• Unforeseeable reactions of various invested parties. → Unknown effects.

Shortterm:
I'm fairly confident that a project fork would throw the community into turmoil. Some developers might leave, some companies may be bankrupted, lots of users would lose money. The community would have to reorganize, work on governance, work out new goals, and rebuild teams. Blocks will slow down due to hash power splitting to two chains. The underdog may use this opportunity to completely redefine themselves, thus bringing their project back into the game. Development would slow down significantly for a while. I would expect each chain to have a lower value than the original chain, most likely the sum of both would fall well below the original chain's value.

Longterm:
I'm convinced that cryptocurrencies benefit so strongly from the network effect, that only a small number of them will be able to coexist, i.e. both blockchains would be competing for the same market share. Either they diversify to an extent where they appeal to vastly different userbases, or balance will at some point tilt, causing one side to take the lion's share. Even if the projects significantly diverge, one should end up much more widespread than the other. Should this schism have a clear victor quick enough, the winner, now improved in comparison to the original blockchain, could attract the bulk of the community, and rally. If they split without a clear majority and the schism drags on, it might become so ugly that both bleed support and go extinct.

^*_{It's not clear that two chains would persist after a hardfork. The game theory seems to work out in a way that one chain would very quickly be abolished.}

I agree with Murch on what would happen if we get a persistent de-facto fork of the blockchain; the sum of both would fall well below the original chain's value.

However, I don't believe we will ever get there. I believe it's a common misconception to think we could ever get a split into "core-coin" and a "classic coin" (or XT coin) with those two being on somehow equal footing. That won't happen. The hard-fork is only reality when;

1. At least 75% of the hashing power signals support for the new chain rules
2. Some grace time period (28 days) have passed, allowing the remaining 25% to upgrade their software
3. Some miner actually mines a block that is not accepted by the old rules (that is, a block that is above 1MB).

And even then the coins won't be split; transactions will still be going into a shared mempool and they are likely to be included on both chains. Now if the split is allowed to continue it will be messy as hell, some transactions going through at both chains and some only at one. Some clever people will probably be doing double-spend-attacks to make sure to split their coins. After a while freshly minted coins will be entering the chains, they will be valid only on the chain they are mined.

That said, I believe the hard-fork, when/if it comes, will be successful - the chain following the old rules will be abandoned, and the BTC value will go through the roof once the market realize that the much-feared-for hard-fork went smooth.

To initiate the count-down for the hard-fork, at least 75% of the miners have to signal support - but in reality the threshold is likely to be higher:

1. Miners depend on a high BTC value, hence they will only be willing to signal support for the hard-fork if it is overwhelmingly probable to be successful. Last I heard, Chinese miners will signal support when it seems likely that at least 90% of the hashing power will support it.
2. Miners will have a very hard time selling their freshly minted coins if they mine at the "wrong" part of the fork - hence whatever minority is against the fork will be very quick on switching sides and support the "winning" side.
3. The "old" fork will for all practical purposes become unusable for several months, even if as much as 25% of the miners still will support it - the everage interval between blocks will be at least 40 minutes, the mempool will become overflooded, transactions won't go through, it will be a sinking ship for sure.