Short answer. No. Article 24 of the Family Code makes it the duty of the local civil registrar to prepare the documents required for a marriage license, and to administer oaths to interested parties, "without any charge in both cases." Neither preparing your documents nor administering the oath may be charged for.
What the law says
It shall be the duty of the local civil registrar to prepare the documents required by this Title, and to administer oaths to all interested parties without any charge in both cases
Family Code, Article 24 — Registrar's Duty to Prepare Documents; Tax Exemption. Read the full provision →
What the law says
The documents and affidavits filed in connection with applications for marriage licenses shall be exempt from documentary stamp tax
Family Code, Article 24 — Registrar's Duty to Prepare Documents; Tax Exemption. Read the full provision →
What Article 24 requires of the local civil registrar
Article 24 of the Family Code states the registrar's duty plainly: "It shall be the duty of the local civil registrar to prepare the documents required by this Title, and to administer oaths to all interested parties without any charge in both cases." Preparing the required documents and administering oaths to the parties involved are both duties the registrar has to perform, not services the registrar may bill for.
'Without any charge in both cases' covers both duties
The phrase "without any charge in both cases" is doing important work — it makes clear that the no-charge rule applies to each of the two duties the sentence just listed: preparing the documents, and administering the oath. Neither one is treated as the free duty while the other carries a fee; both are covered by the same "without any charge" language in the same sentence.
A related exemption for the same documents
Article 24 also addresses a separate cost concern in its second sentence: "The documents and affidavits filed in connection with applications for marriage licenses shall be exempt from documentary stamp tax." On top of the no-charge duty for preparing the documents and administering the oath, the documents and affidavits filed for a marriage license application are themselves exempt from documentary stamp tax.
What this article's protection is specific to
Article 24 is specific to these two duties — preparing the documents required for a marriage license and administering the oath — and to the documentary stamp tax exemption on the documents and affidavits filed for that application. It does not address every possible cost that might come up around getting married; whether some other, unrelated fee could apply to a different part of the process is a separate question this article does not speak to. For those other costs, if any exist, a person would need to look at whatever separate rule or schedule actually governs them, rather than assuming this article's no-charge rule extends that far.