No. eCut is a plugin and requires CorelDRAW to function. There is no standalone version.
Nesting is perhaps eCut’s most famous feature. It automatically arranges your objects on a sheet to minimize waste. Aggressive Optimization Ecut Corel
The most likely search intent for "Ecut Corel" is the for CorelDRAW. This is a professional-grade nesting and cutting optimization tool. Ecut Corel