Unfortunately, cross-game invites will still not work as of 1.60. While players will be able to message each other from within games from 1.60 (in the games that support it), the issue of booting up a different game and then passing on the invitation has not not been resolved. Sony will essentially need to create a new TRC guideline for games to support this. Sony is working on several potential solutions, but in the meantime, this new feature is unlikely to show up for quite a while, and certainly not in the 1.60 update.
To be fair, cross-game invites are not a fundamental feature required for an enjoyable online experience. They are mostly a nice touch to simplify the end-user experience and make it easier for players to interact with their friends. Xbox Live has supported this feature for a while. The issue here for Sony is that it highlights a certain lack of foresight. Features such as in-game buddy messaging can be shoe-horned in at a later time as they are doing relatively painlessly, but more complicated systems such as a cross-game invites require more planning to achieve the expected behavior. Because they require each individual game to be able to deal with them appropriately, they cannot be designed and implemented after the console has launched. Adding new TRCs throughout the lifespan of the console will create a schism between different generations of games, and will only lead to confusion for the consumer. Hopefully will find an elegant way of dealing with this, and any other future problems.
Cross-game voice chat (or game-agnostic voice chat) is another feature now in jeopardy due to lack of planning. The issue again is that it places significant requirements on both processor and memory, which would have to be requisitioned from the game currently being played.