no because this ability itself isn't triggered by an artifact or creature entering the battlefield its triggered by a triggered ability of a permanent you control
A triggers B which triggers C
A - an artifact or creature entering the battlefield
B - triggered ability of a permanent you control caused by A
C - a second trigger of B caused because it was triggered by A
2
2
3
2
A triggers B which triggers C
A - an artifact or creature entering the battlefield
B - triggered ability of a permanent you control caused by A
C - a second trigger of B caused because it was triggered by A