No!

我有一个朋友，是加拿大籍，持有美国绿卡。如果入境美国时，只出示加国护照，不出示绿卡入关，行不行？因为出示绿卡，总有一大堆问题，问为什么不长居美国。

-If he just uses his Canadian passport to enter US, not shows his green card, that means he abandons his green card automatically.