There's some fan support for the process the question proposes...
This 2014 thread suggests the process proposed in the question, but roots the process's legality in the consensus about various supermount builds (originally, I think, from this 2005 thread but also 2010 and 2012). This 2009 thread and this 2011 thread surrender to the topic at hand rather than rehashing (unexplained) arguments forbidding gaining levels beyond those printed. This 2012 thread says such gains are as per the rules as written yet offers no support.
In other words, the Internet thinks it's possible a DM may agree to extend either a less-than-10-level prestige class beyond its printed levels or a 10-level-or-more prestige class beyond its printed levels pre-epic, but a DM can say No and not feel like a jerk.
...But the uncanny trickster's special ability class features probably should neither increase a less-than-10-level prestige class's effective level beyond the class's listed levels nor increase a 10-level-or-more prestige class's effective level beyond 10 pre-epic
The prestige class uncanny trickster (Complete Scoundrel 67-70) at level 2 gains the special ability class features that says
At each level after 1st, you gain class features (including spellcasting ability) and an increase in effective level as if you had also gained a level in a class to which you belonged before adding the prestige class level. You do not, however, gain the benefit of your previous class’s Hit Dice, attack progression, skill points, or saving throws. If you had more than one class before becoming an uncanny trickster, you must decide to which class to add each level for the purpose of determining class features. (67)
Emphasis mine. So it's clear, beyond what's listed, no further guidance is provided elsewhere as to what is granted by an effective level as if.
Further, the Dungeon Master's Guide on Epic Characters says that
Despite the twenty-level limit indicated in the Player’s Handbook, you can advance a class level beyond 20th by using the rules in this book. You can also advance the class level of a ten-level prestige class beyond 10th level, but only if the character level of the advancing character is already 20th or higher. You cannot advance the class level of a class with fewer than ten levels beyond the maximum described for that class, regardless of the character level of the advancing character. (206)
Thus, whether an effective level as if can exceed these limits is the DM's call. Given the hard line the DMG draws, it appears the purpose of the special ability class features probably is neither to allow short prestige classes like uncanny trickster to be extended—especially not infinitely—, nor to allow 10-level-or-more prestige classes to reach levels beyond those printed pre-epic, but, instead, to allow the special ability to do what I expect most people let it do: make a character a little better for what Wizards of the Coast believes is a relatively small price.
Be careful what you wish for
Nevertheless, a player may convince the DM that these ersatz levels do, in fact, extend classes beyond their printed levels. Such a player should be aware that the DM then concocts house rules extending arbitrarily every base class, monster class, and prestige class the DM allows into the campaign.1 That's potentially a lot of work, and the DM might, instead, simply ban the prestige class uncanny trickster (and, by extension, Weapon of Legacy's prestige class legacy champion) for being too much trouble.
With minimum shenanigans, the way it probably really should work (unless the DM says it doesn't)
At level 2 the character can pick to apply the special ability class features to uncanny trickster. This grants the character the benefits of being an effectively as if level 3 uncanny trickster.
Effective as if level 3 of uncanny trickster also includes the special ability class features, but the character can't pick uncanny trickster again—there aren't anymore levels of uncanny trickster to gain—, so the character's stuck applying the second iteration of the special ability class features to a different class.
Finally, were the creature to take the real level 3 of uncanny trickster, the creature'd gain no special abilities from doing so; from his effective level he already had those special abilities.
I suspect even using the uncanny trickster's special ability class features to increase the uncanny trickster's uncanny trickster effective level is an oversight, but there doesn't appear to be any harm in it. The +1 to base attack bonus, +3 to base Reflex saving throws, 3 bonus tricks, 3 favorite tricks, and the special ability tricky defense spread over 2 levels still isn't worth that lone caster level. (However, the extra skill points, Tumble and Use Magic Device as class skills, and d6 Hit Die might have short-term appeal.)
1 A put-upon DM forced to concoct such house rules could extend classes to include entirely new special abilities, like This Player Always Pays for Pizza.
