Short answer: It depends on the layer.
Axons of some neurons in deep layers will project back to L1 (Brecht et al. 2003a, Oberlaender et al. 2011), but neurons of superficial layers extend their axons laterally (Brecht et al. 2003b).
Besides focusing on specific pyramidal cell sub-classes it's worth considering what proportion of inputs to L1 comes from intracolumnar or extracolumnar inputs. From the wikipedia article on the cerebral cortex:
Layer I, the molecular layer, contains few scattered neurons and consists mainly of extensions of apical dendritic tufts of pyramidal neurons and horizontally oriented axons, as well as glial cells. [...] Inputs to the apical tufts are thought to be crucial for the ‘‘feedback interactions in the cerebral cortex involved in associative learning and attention. While it was once thought that the input to layer I came from the cortex itself, it is now realized that layer I across the cerebral cortex mantle receives substantial input from ‘‘matrix or M-type thalamus cells (in contrast to ‘‘core or C-type that go to layer IV).
Most of the inputs to layer 1 (L1) are indeed thought to come from the "non-specific" thalamus and other cortical areas, such as the primary motor cortex in the case of primary sensory areas. I am only aware of circumstantial evidence for the relative prevalence of thalamic inputs in L1. According to staining for different vesicular transporters of glutamate (type I is thought to label mostly cortical neurons in adult animals, type II subcortical), about half of the input to L1 is subcortical (Kubota et al. 2007). It's worth noting that the slender-tufted neurons described by Oberlaender et al. (2011) to project heavily in L1 are considered to be the main targets of the "non-specific" thalamus in the cortex (Brecht et al. 2003a). The extracolumnar origin of cortical inputs to L1 matches with the overall trend observed accross layers for the majority of inputs to come outside the cortical column (Stepanyants et al. 2009).