This entirely depends on how the traffic limitation is implemented.
One way to achieve it is to have a link with 1Mb/s speed. Then, no data will arrive faster than 1Mb/s.
However, modern links are often faster, and the traffic shaping has been implemented in software. Then you should take a hard look at token bucket and leaky bucket. Chances are the rate limiting uses this kind of an algorithm.
Usually, there are buffers, no matter whether the rate limiting is link speed based or implemented in software. How large the buffers are is then another question. Many systems have excessive buffering (bufferbloat).
So, any of these can happen:
- The burst will be immediately allowed in as it's so small (allowing momentary bursts), but if you consider e.g. a 100-second burst, then the burst won't arrive immediately
- The burst will go through 1Mb/s link or software rate limitation, meaning the packets will arrive but later (delay)
- The burst is larger than buffer size, therefore some packets will be lost (loss)
You might think that (2) is better than (3), but the contrary is true. A 10 second buffer is way too large. Nobody likes a link with 10 second latency. It's usually better to have low latency than it's to have low loss.