Can a gene be split between different genomic locations several kb appart?
Yes you can have exons and introns of the same gene separated by hundred (even thousands!) of kilobases.

Here is an example for the human genome:
"On average, there are 8.8 exons and 7.8 introns per gene. About 80% of the exons on each chromosome are &lt; 200 bp in length. &lt; 0.01% of the introns are &lt; 20 bp in length and &lt; 10% of introns are more than 11,000 bp in length."

Source: https://www.ncbi.nlm.nih.gov/pubmed/15217358

For the splicing process, it is not really a problem for the distance. Let me reframe the questions by challenging the assumption you are making: long distances in a sequence correspond to long distance in space.

Actually, DNA/RNA molecules are can have a lot of tertiary structure for example, G quartets for DNA, hairpin structure for RNA.


Source: https://upload.wikimedia.org/wikipedia/commons/5/5d/ATPC_secondary_structure.jpg

Long sequence distances are a poor indication of the real distance in space. Thus although from an engineering point of view it is incredible what molecular splicing can achieve mechanistically speaking. As far as I remember, the length for the intron/exon is important for the efficiency/timing of the splicing process (I might be wrong here on the specifics).