Phew! With all the back-and-forth, this seems to be a really trick one to put to rest.
My simple answer to the question: No.
I'm pretty sure I know what Max is getting at here.
So we have our 'ideal' (infinite bandwidth) burst geneerator that turns 'on' at some very definite time. By 'looking' at this signal with infinite bandwidth you can 'see' where it turns on. Say the turn on is a step up to the peak of the sine. Pick whatever voltage level, the time it passes this is the 'turn on' time.
Now make this more of a 'real' signal by limiting the bandwith, by passing through an ideal brickwall filter. You'll find that there is some signal ('looks' like higher freqs) starting BEFORE the original start time. Also, the 'sharp' step is gone and there's a slope with a 'steepness' similar to the highest passebl freq at a large (larger than the burst) amplitude. So what's the start time now? I know people are going to get their heads mess up by this, but an ideal (zero delay all all freqs, brickwall) filter can produce an output signal before a step in the input (non-causal). This happens most for freqs before the cut-off freq. This is overcome in real filters as time delay (changing phase delay in real analog filters, imposed time delay in digital 'flat phase' filters). My main point here is that, define the 'start' as you will (e.g. passing a certain voltage level).
Now you could substitiute a real world analog filter in place of the ideal one above. Now again you must define where the sine 'starts'.
Now turn the ideal generator on and off (0.01s bursts, 10s burts I don't care) at the SAME point in the 5kHz cycle, and pass it through the filter. You'll get the same 'start' waveform in each case, so however you define the start time, it will always be in the right place.
Now, turn the generator on and off at 'random' points in the cycle. After going through the filter, a simple voltage level 'start' criteria will show you some slight shifts in the start time, as the 'start' waveform will be slightly different. Slightly different obviously doesn't give you *exactly* the same. How closely to the original start time you get depends on the bandwith of the filter. See how time and frequency really are the same thing as far as these things go? Time resolution is bandwidth. To nail an event in time exactly (i.e. infinitely accurate timing) you need infinite bandwidth. BUT remember, this is using your arbitary definition of start as crossing a voltage level. The actual 'start' as far the signal goes is still really the same - it's the definition of 'start' that's bad.
Notice that I have so far NEVER mentioned the digital domain or sampling. You ability to nail a 'start' in time is limited by the bandwidth. When going through digital, you have a very well defined bandwidth limit (given by the sampling rate). However, what you put in, after the anti-alias filter, is what you get out - exactly! So the digitizing process does not affect the time resolution of the 'start' whatsoever - whatever you definition (hence my basic answer of 'no').
Let's take a littel example: Take the ideal generator, pass through the anti-alias filter. Measure the 'start' time (or time between bursts if you like - get's rid of delays) here in the analog domain, using whatever measure you like. Now pass the signal through the A/D then D/A and reconstruction filter and measure the 'start' time (or burst interval) for this. You will get the exact same answer, to a resolution less than the sample period! To be clear, the burst interval, or start time, is NOT rounded to the nearest sample period, or affected by the exact timing of the sampling.
Now to go the final step beyond the original question, and go into real audio, as audio gear is bandwidth limited, you can only ever define the 'start' of a signal to within a limit set by the bandwidth.
Of couse another answer is that signals never start or end