If you are interested in conveying formality, T-V distinction is just one of the ways to do it. Formality/familiarity can be also expressed via morphological features (e.g. conjugation) or discourse (choice of words).
Japanese is an example of a language that relies on morphology to convey formality: Keigo (敬語), a respectful language widely used even in everyday speech (in the shops, companies, etc.). To be a bit more precise, keigo is a mix of morphology (special conjugation, words beautification via prefixes) and discourse (highly indirect speech, use of special 'polite' or 'humble' words). Japanese also does not lack 2nd person pronouns, but their patterns of usage are different from European languages.
English is an example of a language that conveys formality mostly via word choice and style. See this page for some examples of differences between formal and informal English.
Russian in addition to T-V distinction, morphology, and discourse uses names to convey formality. Almost every Russian name has several forms: formal, or official, and short (short forms are virtually unlimited in number as they can be created using some common rules). It is very important to use the correct form of a name because different forms are associated with different types of relationships between people and may convey specific emotions. Incorrect use of a short form can be seen as an insult. This concept can be a bit difficult to understand, so let me bring some examples:
- Ivan1 Petrovich Sidorov [Given name + Patronymic + Surname] is a full legal name that is used in official correspondence as a signature or reference to someone; cannot be used as a direct address;
- Sidorov Ivan Petrovich [Surname + Given name + Patronymic] is a form used in most legal documents; can also be used when scolding someone using sarcasm or by parents when seriously reprimanding a child; outside of legal context this form sounds very unnatural and impolite;
- Ivan Petrovich [Given name + Patronymic] is a formal address (can be used in conversations with this man or about this man);
- Ivan is a full form of a given name; traditionally could be used only in formal situations when addressing people of much lower status (children or servants) with whom the speaker is only slightly familiar, modern usage mimics usage of given names in English-speaking countries; implies distance, formality, and emotional indifference;
- Vanya is a common short form of Ivan, it is rather neutral and can be used when talking to friends or children;
- Vanyusha is a short form that conveys warmth, usually used when talking to children; it would be very inappropriate for a man/male teenager to use this form to talk about or to address another man/teenager;
- Van'ka is a common short form that has slightly negative connotations and may express some degree of annoyance and/or dissatisfaction;
- Vanyok is a short form that male teenagers or young adults may use when talking among themselves; sounds a bit rude and normally is not used in conversations that include women and/or people of higher social status;
- Vanechka is a short form that is used for children by older generation family members or sometimes by younger women when talking about their boyfriends; this form implies a close and loving relationship.
Going back to your question, T-V distinction is not strictly necessary for conveying formality. Your language can have separate singular and plural pronouns but not rely on them to express politeness. For example, your language may opt for using those pronouns only in situations where the recipients of the message are unknown (as in Japanese). Or use inflexions to convey formality (Russian, Japanese, French, etc.). Style (as in English and Japanese), names (as in Russian), or honorifics (as in many Asian languages) can also serve this purpose.
1 'I' is pronounced as 'i' in is [do not not confuse with 'i' in idle]