Are cytotoxic (killer) T-cells always present or are they only produced during a cell mediated immune response?
Naive T cells are regularly matured in the thymus where they're released into the blood. A majority are CD4+, but many are also CD8+. As a caveat, many are TCRαß+, and few are TCRyδ+ (outside the scope here but fun to look up and read).  From there, they home to the lymph node where they hang in the T cell zone until blood trafficking signals coax them into the blood. T cells regularly navigate the body in response to signals from different cells such as blood vessel endothelium, lymphaptic vessel endothelium, epithelial cells, and so forth (1). 

The basic process behind an adaptive immune response is that antigen-presenting cells get ahold of foreign antigens and head back to the lymphoid organs like lymph nodes. By the time they get there, they've matured into "licensed" professional antigen-presenting cells. They interact with both CD4+ or helper T cells, and CD8+ or cytotoxic T cells. It's more complex than that, but the point of the helper T cell is to produce "help" signals. These include IL-2, and other cytokines which not only assist the CD8+ T cells in their activation, but also determine a lineage they'll take based on other factors. 

So they're both there, in the lymph node at the time the antigen-presenting cell, such as a dendritic cell, arrives to activate the lymphocytes in that region. Take home point: the naive lymphocytes are there until they are activated, in which you would be correct in your last line. But they do actually do things other than sit there, other take home point. They aren't simply anergic and waiting.