Will transactional replication break if there is a heavy update/delete query run on the publisher DB
Sounds like you were attempting to perform the delete operation in a single transaction.  This being the case, the answer is "Yes, it will most likely break."  

Even without replication, it's a bad idea to do such a large operation in a single batch.  You would be better off looping a smaller number of deletes - it's faster and less of a performance issue.  If you do this, the answer is, "No, it shouldn't be a problem."

Here's an example

Declare @keepGoing bit
set @keepGoing = 1

while @keepGoing =1
begin

    if (select top 1 from someTable) is null
        set @keepGoing = 0
    else
        delete sometable where ID in (select top 10000 ID from sometable)

end