Yes, essential oil blends can provide an effective replacement, for cosmetic preservative; all depends on the policy of the company manufacturing the cosmetic
Find attached an article and a review of essential oil as preservatives
You can go through the paper, "Plant essential oils as food preservatives to control moulds, mycotoxin contamination and oxidative deterioration of agri-food commodities – Potentials and challenges"
by Bhanu Prakash, N.K.Dubey
But practically by my experience the precentage of essential oil determines its preservative nature.
They "can" but there are many challenges in application. Their efficacy is poorly described - so active component(s) and concentrations required for efficacy are not known. As they typically vary in composition from batch to batch, prev efficacy data may not be representative of efficacy in application whatever is published. You really need to qualify every batch - anaytically or by pres testing. Safety-wise - there's no way to addrs every component.
I'll add the articles most enthusiastically saying "yes" are usually from academics and others who've never had to preserve a product and take responsibility for its continuing quality.