Hello David,
Yes!
The great thing about .gz files is that you can combine them directly. For example
cat file1.fastq.gz file2.fastq.gz file3.fastq.gz > files1-3.fastq.gz
that will merge all three files.
Or ever better
cat *fastq.gz > all.fastq.gz
will merge every file that ends with fastq.gz.
Let me know if this works for you!
Colin