Yes, I think so.
They are only amplified linearly so there won't be much unless the template is cloned DNA (the specific template is then present in large amounts). If the template is genomic DNA, the sizes will be so varied that it will disappear into a smear, or up at sizes larger than the gel can resolve.
However, I think that if the template were a fragment of cloned DNA, for example .1 ug of a DNA strand that ends .3 kb from the "primer", then after cycling you would generate a large amount of single stranded DNA 300bp + the primer size. So in that specific case you might actually generate something you could see on the gel. As I said earlier, it would be single standed, so it would run differently than the size marker ladder, and might be fuzzy, or have multiple bands if the DNA folded into secondary structures.
I'm not sure why more plasmid sized product isn't generated on ciruclar plasmid template, such as when I PCR a large gene on the plasmid. Maybe the extension time isn't enough, although at 5kb that's a large % of the plasmid itself and the PCR product was generated. It may also be that when I do mutagenesis with two primers complementary to each other with the mutation in the center, and "PCR" (not really since it is linear) I think I use a lower extension temperature. I think I use 68C instead of 72. I think this was to prevent strand displacement. With stand displacement the strand extension wouldn't stop at a certain spot where it hits the annealed primer, but could continue around and around the plasmid, and would not make a specific size band. But, I'm not sure 4 degrees would make that much difference. Maybe it's just not very efficient making something so big, and with only linear amplification it's not enough to see.
Whenever any PCR is done, both strands of the PCR product may act as primers in future cycles. The reason a distinct PCR product band is seen is because so much product is generated by the geometric amplification, that it soon exceeds the amount of all other homologous template present, and finds nowhere else to prime. (I'm probably restating what you or I have already said.) In the background of PCR on any larger template, there must be some amount of larger strands generated.