Short Answer: No, it cannot disclaim a contract of adhesion.
(I ask because I increasingly see in advertising or promotion that a
company says that you can have their service without a contract and
Most legal words have more than one meaning depending upon the context. The term "contract" is no exception.
In this context, as used in an advertisement or promotion, what "service with a contract" means is service without an "executory contract" (which means a contract that hasn't yet been fully performed when agreed to), for a fixed term, while "service without a contract" means a contract that can be terminated at will or when the amount currently paid for the service is exhausted.
But, in the more general sense that the term contract is usually used in the law, you still have a contract, even though it can be terminated at any time, and either party could sue the other for a breach of contract in court (or in an arbitration forum if the agreement contains an arbitration clause as it often does).
Incidentally, a "contract of adhesion" is a take it or leave it contract, used in many individuals transactions, drafted by the party with more economic power that the party with less economic power must accept to get the service and cannot negotiate the terms of. Status as a contract of adhesion doesn't not dependent upon one's status as an entity or an individual. The contract you describe is almost surely a contract of adhesion, but not for the reasons that you provide.
An entity could be bound by a contract of adhesion and contracts of adhesion are usually enforceable if their terms of reasonably related to the subject matter. A contract of adhesion is not automatically invalid and cannot be disavowed unless it is "unconscionable" (i.e. absurdly unfair and exploitive) and even then such invalidity might be applied to a particular term of the contract of adhesion, rather than to the agreement as a whole.
All contracts drafted by the other party are construed against the drafter in cases of ambiguity. This is not limited to contracts of adhesion, although all contracts of adhesion, by definition, are subject to this rule.