No, because although it is mathematically 2Gbit/s, the second connection is actually to be seen as pure redundancy. In total, the bandwidth remains at 1Gbit/s. The exception would be if your switch supports link aggregation, then you can expect more bandwidth.
Alternative. You can unofficially upgrade the Synology with 2.5GbE via USB. But in the end, this is only useful if the NAS or the hard disks can provide this.