No. It is possible to ensure that people don't cheat even with FOSS; signing and encryption make it possible to set up a nice relatively-difficult barrier to cheating. There are dozens of parallel projects that demonstrate this; perhaps the most obvious is Bitcoin. There are breakins with Bitcoin, but the threshold is very high, and it's pretty clear that only the most intelligent and savvy attackers make off with cash.

In general, people sometimes ask this question about FOSS and security. Isn't FOSS bad for security, they say, since attackers can look at your code and find the holes so they can break in? What this assumes is that the holes are inevitable and obvious, and all anyone needs to break in is find them. It turns out that this isn't true, as many security-sensitive open source projects from OpenBSD to Mozilla Firefox have demonstrated. Security holes shouldn't exist; help from the community to prevent this is key. The hope that code will be more secure if we only keep it secret - otherwise known as "security through obscurity" - is a pipe dream.

It is reasonable and possible to program these games in such a way that the client is assumed to be malicious, but this is not a common practice. Preventing cheating would be possible in the general case. For most existing games, though, a modified client already enables the user to cheat. It is just more difficult to create it without the source.

I think this is the most important question regarding online games on Linux, and aren't most games online these days?

I think that the solution is radical: I think that as much much time and effort should be put into making the binary unhackable as is put into the game. Ultimately, DRM(1) is a game, and a lot of programmers are addicted to breaking it anyway.

What's funny about DRM in the case of an online game is that it's actually a feature that customers would pay extra for, and a premium for quality DRM. Hopefully, we'll have good companies and groups creating it, and online games (whether given away or sold) will advertise and brag about what kind of DRM that they're using.

(1) I'm using the term DRM because I can't figure out a better term - but it's more like tamper management, isn't it?

Technical solutions for social problems are tricky.

Putting stuff server side might help - meaning it doesn't matter so much what client people are using.