No, results won't be returned in the same order, even without a plan change. The query executor does not have to reorder the rows, it doesn't even order them in the first place.
For example, when rows come in disk order:
CREATE TABLE o(id int);
INSERT INTO o VALUES (1),(2),(3);
ANALYZE o;
EXPLAIN SELECT * FROM o;
QUERY PLAN
-------------------------------------------------
Seq Scan on o (cost=0.00..1.03 rows=3 width=4)
SELECT * FROM o;
Result:
id ---- 1 2 3
Let's update a row (without even changing the value):
UPDATE o SET id=2 WHERE id=2;
and rerun the same select:
SELECT * FROM o;
id ---- 1 3 2
Notice how the order has changed. Of course the plan is still the same:
EXPLAIN SELECT * FROM o;
QUERY PLAN
-------------------------------------------------
Seq Scan on o (cost=0.00..1.03 rows=3 width=4)
Conclusion: the execution plan doesn't imply any order without order by
.