Are sealed lead-acid batteries safe to use indoors?

Actually SLA batteries have a vent... so the name "sealed" is a bit of a misnomer. VRLA (valve-regulated lead-acid battery) is actually a name for the same tech.

Practically every UPS (uninterruptible power supply) I know of has one [or more] SLA[s] inside, so it's generally safe for indoor use. Here's a snippet from an APC white paper on the issue:

Valve regulated lead acid (VRLA) batteries [...] do not require special battery rooms and are suitable for use in an office environment. Air changes designed for human occupancy normally exceed the requirements for VRLA [...] ventilation. Vented (flooded) batteries, which release hydrogen gas continuously, require a dedicated battery room with ventilation separate from the rest of the building.

And bit later in the paper the difference in gas output is quantified as 60 times less for VRLA:

VRLA batteries are considered to be “sealed” because they normally do not allow for the addition or loss of liquid. A vented battery can give off sixty times more gas than a VRLA battery in normal use.

And the reason for this is that in a "sealed"/VRLA battery:

hydrogen recombines under pressure with oxygen into water inside the battery. Gas can only escape when internal pressure exceeds the rating of the pressure valve.

The fact that they're pressurized explains why in extreme cases of misuse or abuse they end up seriously bulged. The plastic container is actually designed to cope with that scenario.

Also, small SLAs (almost certainly the one you have) use gel as electrolyte suspender so won't spill liquid[s] even if cracked. The larger ones use a glass mat instead (gel is rather expensive).

Yes, sealed-lead batteries are considered safe for indoor use -- they are no different from dry cells or NiCds in that regard, and can be found in emergency lights and other applications where low cost and relatively long livespan in float applications is critical.

With that in mind, it is possible (although unlikely) to encounter leakage if they are left untended for very long periods of time (just like dry cells).