Explanation
No. Establishing an embassy does not turn its premises into the sovereign territory of the country it represents. The premises remain within the host state's territory while receiving special diplomatic protections.
Article 21 of the Vienna Convention on Diplomatic Relations places mission premises within the receiving state's territory. The UK's Crown Prosecution Service explicitly confirms that diplomatic premises in the UK remain UK territory. Legal analysis published by Völkerrechtsblog likewise distinguishes diplomatic privileges from territorial sovereignty.
Ownership and sovereignty are different. A sending state may own or lease embassy premises without gaining sovereign territory. The premises' inviolability restricts entry and other enforcement measures by host authorities; it does not redraw the international border.
Key takeaway
An embassy is protected diplomatic premises within the host country, not a separate piece of the sending country's sovereign territory.