A one-liner using a conditional is as close as you can come.
cd /path/to/output && split --bytes=1024M /path/to/input/filename && gzip x*
gzip will only run if split is successful because of the conditional && which is also between the cd and split making sure the cd is successful, too.. Note that split and gzip output to the current directory instead of having the ability to specify the output directory. You can make the directory, if needed:
mkdir -p /path/to/output && cd /path/to/output && split --bytes=1024M /path/to/input/filename && gzip x*
To put it all back together:
gunzip /path/to/files/x* && cat /path/to/files/x* > /path/to/dest/filename