Note: I'm using Wikipedia as my only source. This answer is supposition. But let's think this idea of retreat through.
...he thinks that the retreat of the Red Army in the early phases of the war was part of Stalin's strategy.
Was there a grand strategy?
The defenders in the fortress were surprised on the first day of the invasion by a brief, but heavy, early morning bombardment by the 45th Infantry Division followed quickly by an sudden infantry attack. The Germans were crossing the river within minutes before the Soviets could mount an effective defense. They couldn't effectively man and defend their outer defenses. The Soviet defenders that didn't make it back to the fortress were caught in the open, or stuck in isolated strongholds. Vital men and material and good defensive ground that could have been used to resist a siege were lost.
This was in the first few hours. If this was all part of Stalin's grand strategy, it stank. If an attack was coming and retreat was the plan, nobody told the defenders of the fortress. How can they plan a retreat from an attack they didn't know was coming?
Furthermore, Soviet high command wasn't aware that Brest was holding out.
In March 1942 the Red Army defeated the [the 45th Infantry Division who conducted the siege] at Livny, Russia and captured the archive of the division. That was the first time the Red Army learned about the defense of Brest Fortress.
The Soviet High Command can't coordinate a retreat from a siege they don't even know was happening.
Given there is no evidence of a coordinated grand strategy of retreat, this comes down to the tactical decisions of the local commanders. Once the surprise wore off, should they have held out, or should they have attempted a breakout? Let's look at the situation at the end of the first day.
The units in the Fortress were the 6th Rifle Division, elements of the 42nd Rifles, plus some Soviet Border Troops. The 6th was assigned to the fortress and was mostly fully formed up when the attack hit. By the end of the first day the bulk of the 6th and its HQ had retreated, though scattered, but some elements remained trapped in the fortress.
The 42nd was still forming up when the attack came having only collected about 3/5ths of their strength and who knows what equipment. Their elements were scattered around with only part of the division inside the fortress. The surprise attack only made this worse. Some elements of the 42nd did break out on the first day, but fractured elements were scattered about inside the fortress.
Finally, the Soviet Border Troops trapped within the fortress were not part of the regular army. These were NKVD, a completely different chain of command.
At the end of the day many forces have retreated. Inside the fortress is the remnants of the 6th division with no divisional HQ, elements of the 42nd division which didn't even complete muster before the war started, some border troops under the NKVD. They have who knows what equipment, ammunition, probably few vehicles, armor, or artillery. They're scattered, surprised, and have taken heavy losses. Their command and communications are fragmented. They may only have a hazy idea of the strategic situation, what direction the front line is, and how far. They're surrounded by superior, mobile German forces.
In this desperate tactical situation, organizing a coordinated break out among the fragmented defenders would be difficult to say the least. Its chances of success were even less. And break out to where? The rest of the Soviet army was also getting mauled and fast retreating. All they would succeed in doing is leaving their strong defenses to be scattered and slaughtered in the open.
The local commanders made the correct choice to remain behind their defenses and hold out for as long as possible.
Was it effective? Probably more effective than getting caught in the open, surrounded, and annihilated like much of the rest of the Soviet border army.
But what about the casualty ratio? 2000 dead & 6800 captured Soviets for 429 dead and 668 wounded Germans seems a very poor trade off for a siege. And it is. And they didn't even block the railway and roads to Moscow.
However, they held up a German infantry division, and elements of others, for 7 days. That's probably 7 days more than they would have otherwise if they attempted a breakout. Given the tight timetable of Operation Barbarossa, any delay is a Soviet strategic victory.