Sure. Not a whole lot, but you'll get a decent number.
Beer et al. 2004 present a formula for calculating the mean time before a star passes within a distance $b_{\text{min}}$ of another star:
$$\tau=7\times10^8\left(\frac{n}{10^5\text{ pc}^{-3}}\right)^{-1}\left(\frac{b_{\text{min}}}{\text{AU}}\right)^{-1}\left(\frac{M}{M_{\odot}}\right)^{-1}\frac{v_{\infty}}{10\text{ km s}^{-1}}\text{ years}$$
where $n$ is the local stellar number density, $M$ is the combined mass of the stars and planet, and $v_{\infty}$ is the velocity of the intruding star when it is far away.
It looks like M60-UCD1 has a number density of $n\sim3.4\times10^3$ per cubic parsec. Let's say the star and the perturber are both red dwarfs (hence the orbiting planet can be tightly bound and still remain in the parent star's habitable zone). Say the planet will be severely perturbed if $b_{\text{min}}=100\text{ AU}$. A decent estimate of $M$ is $M\approx0.4M_{\odot}$. We then get $\tau\approx5\times10^8$ years. This may be a bit conservative - I suspect that $b_{\text{min}}$ could be smaller by a factor of a few - so we'll maybe increase this to about 1 billion years.
(I should add that I used a number density from Wikipedia, if we use yours (the number density can be found from the mean separation as roughly $n\sim l^{-3}$), we can a timescale lower by a factor of about 2. That's not terrible. Factors of 2 are often ignorable in astronomy. An order of magnitude difference - well, that would be problematic.)
A billion years or so isn't bad. Not a significantly short time. Life took a couple billion years to develop on Earth, but that's not necessarily representative of all planets. Besides, this is merely an average timescale. Plenty of planets in the galaxy will be disrupted sooner, and plenty will be disrupted later, if at all. Yes, they could form, and yes, a number would survive long enough for life to develop, if it had the chance to begin.
How many planets?
M60-UCD1 has a stellar mass of about 200 million stellar masses. Let's say that translates into 300 million stars. Maybe 10% of those form planets. You now have about 30 million planets. Now, the majority of these stars will be red dwarfs; you'll see comparatively few Sun-like stars - low-mass stars are simply much more likely to form. If even 1% of those have planets that survive a couple times longer than expected, you should have a few hundred thousands of planets, most around red dwarfs. If even 1% of these are habitable, you still have thousands of systems that may develop life.
I'll definitely need to update this section with some literature-supported numbers, but I'll note that I was very conservative, I think, with some of these numbers.
Supernovae may not be a problem
Now, we still have one question to answer, which DWKrauss pointed out earlier: What about nearby supernovae? The minimum distance for a typical supernova to have severe impacts is in the vicinity of 8 parsecs. Given the above number density, there should be about 1.78 million stars within that distance. For a Milky Way-like present-day mass function, that should produce about 7-8 stars which will become supernovae - not great!
That said, that's an overestimate. Recent work (Dabringhausen et al. 2008, Mieske & Kroupa 2008) indicates that ultracompact dwarfs have an extremely high mass-to-light ratio. Unless there's a high proportion of nonluminous matter (possibly dark matter - that hypothesis for the $M/L$ ratio hasn't been ruled out), that means that our stellar population models are wrong. Now, this in turn has two explanations. The first is that there are plenty of dim stellar remnants - neutron stars, black holes, etc. - floating around. After all, many of these galaxies are old, and unless something triggers a new round of star formation, many massive stars exploded long ago. If there's little star formation, then our estimate of the supernova threat was an overestimate.
The other possibility is also enticing. It holds that the mass function is what's called bottom-heavy - in other words, there's an extreme number of low-mass stars. One big reason that's possible is that ultracompact dwarfs are nothing like the Milky Way, and it's quite likely that their mass functions are quite different from ours. A bottom-heavy mass function would explain the observed $M/L$ ratios well - and would indicate that our estimate for nearby supernova-producing stars is way too large.
