I would say there are several variables concerning that question:
1. Is the pump pressure rated or non-pressure rated? A pressure rated would handle it better.
2. Who makes the pump? Different manufacturers handle extra heat/load better than others.
3. It will cause the pump to work harder and generate more energy waste than is necessary.
4. Very important is the length of the run of 1" versus 1 1/2" piping. Use the calculators on reefcentral to do a few size/pump/flow calculations and check the results.
5. What size does the pump recommend? Some pumps even say the line/plumbing should be larger than the outlet/inlet. This can cause unneeded bubbles/cavatation in more extreme cases especially for the pump inlet size.
Given the caveats above, I'd hazard a guess that it probably *won't burn up* the pump, but you would be better served by getting a better match if you aren't considering enlarging the pipe size. JMO
Doug