Yes, this is well known in the literature. High glycemic foods increase sebum production. (High protein diets do too by the way because of IGF-1.)
Some sources on this:
"Sebaceous gland lipids" by M. Picardo et al:
Low glycemic load diet has been demonstrated to be able to correct the increased sebum production [...] All these findings suggest that dietary habits, supplying substrates for the sebaceous lipid synthesis, can be involved in the sebum production mechanism. [...] caloric restriction has been shown to dramatically decrease the sebum secretion rate.
On high-protein diets (IGF-1 raises are caused by both carb/sugar and protein) causing the same issue (Vora at el: "Correlation of facial sebum to serum insulin-like growth factor-1 in patients with acne"):
It was seen that there was a positive correlation between the amount of MFSE and serum IGF-1 (Fig. 1; R2 = 0.69; P = 0.0001). Moreover, this was true in both men and women (Table 1). It has recently been shown that IGF-1 can increase lipid production in sebocytes in vitro via the activation of IGF-1 receptor through multiple pathways. 8 Together, our data suggest that increased IGF-1 could lead to increased sebum secretion.
Insulin induces an increase in the size and number of sebocytes, as well as lipogenesis and inflammatory response
Source: "Insulin and the sebaceous gland function" by Okoro et al
The high prevalence rates of adolescent acne cannot be explained by the predominance of genetic factors but by the influence of a Western diet that overstimulates the key conductor of metabolism, the nutrient- and growth factor-sensitive kinase mTORC1. Increased mTORC1 activity has been detected in lesional skin and sebaceous glands of acne patients compared with acne-free controls.
Source: "Acne vulgaris: The metabolic syndrome of the pilosebaceous follicle" by Melnik
In conclusion, we demonstrated that specific dietary patterns were associated with sebum content, skin hydration and pH in healthy Korean adults and that those associations were affected by sex.
Source: "Dietary Patterns Associated with Sebum Content, Skin Hydration and pH, and Their Sex-Dependent Differences in Healthy Korean Adults" by Lim et al.
But the correlation between diet and sebum is not the only interesting aspect about this.
In fact, sebum production rates and Androgenetic Alopecia are also connected:
There is a very strong correlation between sebum level and severity of Androgenetic Alopecia.
source: "Correlation between sebum level and severity of male androgenetic alopecia" by Tambulan et al.
From "Scalp Biophysical Characteristics in Males with Androgenetic Alopecia: A Comparative Study with Healthy Controls" by Chanprapaph et al:
Androgenetic Alopecia-affected areas show [...] larger sebaceous glands producing more sebum
I have covered this topic, among others, in the PDF document attached to
the post titled "Original research theory: How Androgenetic Alopecia is a manifestation of insulin resistance and its connections with CVD & PCOS" where I summarize all findings related to the connection between diet, lifestyle and hair loss. You can find it in the research section.