I have a 1000w generator. Can I run a cord from the generator to a 110 outlet to power the boiler in my home?

First, you must check the load to make sure the generator will handle it. Yes, you can but it is not a good idea because you will be also supplying power to your entire house grid, unless you are careful and isolate everything else. Boiler power may be controls, pump, and fan. May be better to isolate it from the rest of the system.