Is there a time limit in The Ur-Quan Masters?

Strictly speaking, yes there is a time limit... (spoiler warning) The game is intelligently written and scripted to respond interactively to the decisions made by the player. You may play nice and fall into the role of The One, or you can be a bit of a jerk. Your decisions may cause certain other races to leave our galaxy, or may cause the destruction and extermination of another race, and much more. Its part of the rich story telling aspect of the game which is the best part for me imho. But these are subplots and doesn't affect the main plot. Which means they're more like timed events served to advance the story. So you should be disappointed if you are expecting multiple story endings like Fallout. As i said the timer feature still applies, but the good news is that almost in any style of game play, you shall find more than enough time to complete the mission. Now, go play this epic game and enjoy. (p.s. I will take a minute of vigil tonight in memory of the atrocity of Activision in its brutal killing of such an esteemed title.)

TL;DR and nonspoilered: YES, but it's a very large limit so there's no real need to rush.

Full answer in spoilers. LOTS AND LOTS OF SPOILERS.

Unfortunately

Once that happens,

As it happens,

... which is the Non-Standard Game Over.

ETA: According to this link (Spoiler warning) you have roughly 4.5 in-game years before the clock starts ticking to failure; time passes at a rate of one day every thirty seconds in interplanetary space and one day every five seconds in hyperspace/SPOILERSPACE. (Thanks to Kaffeleif for the addendum)

So math-wise you have about 13 hours of gameplay in hyperspace to finish the game. The game is 4.5 years (4.5*356 days = 1642.5 days), and each day is 30 seconds in hyperspace 1642.5*30 seconds = 821 minutes, or 13.6875