Refresh token is essentialy a credential reference, that your client can exchange for access token, when there is no active user session.
For example if you want to periodicaly sync issues from Github with your inhouse system.
It is often misused like some kind of session. It is essential to diffirentiate those things. And scope name offline_access is there for a reason.
So in simple cases - you just rely on OP session and get new token with authorize/token endpoints combo. You should not be prompted to provide credentials as long as session is alive and consent is given for that particular app.
If you need to do some backgound stuff - ask for refresh token also.
As for question: no.
EDIT(More in-depth explanation):
if we are talking about web there are two main cases:
Client that can securely store secrets like usual web app with server page rendering and clients, that cant store secrets, like SPA apps. From that perspective there are two main flows (omitting hybrid to not over-complicate): Authorization Code Flow and Implicit Flow respectively.
Authorization Code Flow
On first request your app checks it own session(client session) and if there is none - redirects to external OP(OpenID Connect provider) authorize url. OP authenticates user according to requirements expressed in request, gathers consent and other stuff and returns authorization code. Then client asks token endpoint with it and receives access_token/id_token pair with optional refresh token if user granted offline access consent. This is important, because user can deny it for your app. After this client can request userInfo endpoint to get all user claims that were granted during consent. Those claims represent user identity and do not contain stuff like authentication method, acr etc. Those claims present in id_token alongside with expiration for example. After that client starts it own session and have option to set its lifetime equal to id_token lifetime or use it own to provide smooth UX for example. At this point you can discard access_token and id_token at all if you don't need access to other APIs(like all scopes in access_token are specific to OP and subject). If you need access to some API you can store access_token and use it for access. It becomes invalid - redirect to OP for new one. Expiration can be more lax here, because of more secure environment on server. So even 1hr is an option. No refresh tokens used at all.
Implicit Flow
In this case your lets say Angular app redirects to OP, gets its id_token and optional access_token from authorize endpoint directly and uses it to access some APIs. On every request expiration is checked an if needed, client sends request to OP in hidden iFrame, so there won't be any visible redirects as long as OP session is alive. There are some great libs for that like openid-client.js. No refresh is allowed here at all.
It is important to differentiate client session from OP session, token lifetime and session lifetime.
To address some specific needs there is Hybrid Flow. It can be used to get authorization code and id_token for your session in one request. No chit chat over network.
So when you think about refresh token just check your needs and map them to a spec :) And if you need it anyway - store it as secure as you can.