Yes, you can use a wound healing drug to promote fibroblast cell growth in vitro. However, when using, attention should be paid to the content of some drugs and the conditions required when playing the effect, and the specific situation needs to be further verified by experiments

Wound healing is a complicated process. Many drugs and factors including that increase inflammation and angiogenesis, stimulate fibroblast proliferation and collagen production and promote epithelialiization may affect the outcomes of healing. If the role of this drug is to promote fibroblast proliferation, you can use it to increase fibroblast proliferation in cell culture medium in vitro. in this case, why you just add bFGF to the medium instead.

I am not entirely clear how you wish to use your 'drug'.

Assuming that it is a small molecule 'drug' you can use it to supplement any serum-free media formulation. We published a protocol for this 15 years ago: see doi: 10.1089/ten.tec.2007.0428. Lonza purchased the rights to our formulation, but buried it when they introduced their Serum-replacement formulation. They have since improved this further with their BulletKit® formulations.

Recommend that you dig into the literature from the mid-late '00s for protocols. Accurate formulation concentrations and absence/presence of drug-binding species is going to be critical. Make sure that it does not alter the pH, osmolarity, and osmolality!