Well the 3DS has two kinds of game updates:
1) Update Data
is in the form of Update Data, which is what games like Mario Kart 7, Super Smash Bros., Terraria, and Shovel Knight use.
This means that you download a patch and it applies it in such a way where it has it's own title and can be downloaded from the 3DS eShop, free of charge weather the game is installed or not. Typically this is used for games that are large in size, and often for games with physical releases, but is not limited to physical release games. Some games, such as SmileBASIC use this method anyway, I believe it is up to the developer how they want to handle this stuff.
2) Full Title Update
This is in the form of the actual title on the 3DS eShop server being updated itself, and requires users to reinstall the entire game, overwriting the previous version. This is how games like 1001 spikes, Ironfall Invasion, Colors 3D, and a fairly sized pool of smaller eShop titles are updated. These require your 3DS have a valid ticket for downloading the game from the eShop, if the CIA you installed has a valid ticket in it, then this will work for you, however, most CIAs that are in popular distribution locations do not contain valid tickets, and when downloading the game, will error out at 99%. This will require you to either use one of the CDN methods for installing titles, such as freeShop or FBI with QR Codes from a particular site, or you can simply find an updated CIA, which is a tad on the harder side to accomplish.
As you can see, in either case, the answer is yes, you can update, but one is clearly easier than the other.