Depending on the registrars, the change should not be visible. However, if a registrar ceases to provide the NS1, NS2, etc information to the name resolution requests, you can have your domains hosted anywhere, nobody will know which authoritative server to ask, if no non-authoritative has the IP addresses cached.
One thinkg that could be done, if you have such control and know that none of you servers will change IP address for a while is to change the TTL, or time to live. If you give a long TTL for each domain, this means that anyone who resolved the IP address previously will cache it for much longer, without re-querying the authoritative domain name servers. The TTL can be setup in different ways, depending on how the name servers are configured and hosted. If you have full control, using zone files, for example, you can change the TTL for any domain either globally for the zone (or domain) or individually for each host.
Some name service providers such as Go Daddy give full DNS control, but over a web interface. There, for each entry, you can change the TTL. However, you are limited to what he offers you, not what you can put in the zone file.
Once the registration transferred to a new registrar, you can then get back to each of your domain or zone file, and change the TTL to a more reasonable duration, such as an hour or 24 hours.
In CANADA (for .ca domains), when you transfer a domain to a new registrar, CIRA (Canadian Internet Registration Authority) will email the administrative contact of a given domain, asking to confirm a domain transfer to the new registrar. This may be different for other general top-level domains (TLD) such as .COM, .NET, .ORG or country-based top-level domains.
You can find more about this and other DNS matters by searching on the web, for terms like "zone file" DNS, "time to live", "registrar", "authoritative". You will then find more information than you want about it.
In short, when you change registrar, there is no warranty of no-downtime, because there is no warranty that the old registrar will release the control over your domain to another registrar with any fuss.