The short answer is perhaps: yes, but not one you'd want. IMO there are two ways around this problem:
1. Apply dynamic range control
Probably what you were thinking of here. This would apply dynamic range control (e.g. a limiter) across your (entire) pulse output. I've not tried this (for reasons see below) but I'd venture your best route would be a LADSPA plugin, as per this answer. Once configured, any transient bursts in volume (over the threshold level) should cause a reduction in volume (by a ratio) on the output meaning your tweeters should get saved. Note that this almost certainly won't apply to Dolby or DTS audio e.g. from a DVD / BluRay on the PC.
Of course, the problem is when it kicks in during that sudden bit in the film, or a big crescendo in a symphony. Essentially all (aggressive) dynamic range control is horrible for music (with certain notable exceptions), so I'd highly recommend against it here especially as you have (had?!) decent speakers. So the other option...
or: 2. Make sure the spikes don't happen
This may sound naïve but there is some mileage in this route. Whilst traditionally engineers often recommend the (power) amp stages be left on maximum, leaving volume control nearer the source, in a digital setup there is often greater variance in input volume.
Personally, I'd recommend leaving all but your final master volume control on or near maximum, especially any application ones (e.g. movie players, music programs). Final volume control can be with the master control, or perhaps better still using your amp's control.
Additionally, as you may already know, using
pavucontrol (available in Ubuntu repositories). You can tell Pulse to have the system sounds much quieter, and as shown you can also configure the volume for your browser plugins to be lower than your music players', which is generally a good idea, especially if you use ReplayGain (also a good idea...). These really does limit the "surprise" element of those types of web ads (typically delivered by flash, which comes under
plugin-container), and also events out the blarey youtube effect.
With careful tweaking you should be able to set your system up in a way that will minimise the risk of this ever happening again. Good luck!