Is trembling an advantageous response during periods of anxiety?
Some assumptions made in the question.

There is an implicit assumption in your question which I don't think to be correct: you assume that any reaction of the human organism to stress (let's substitute "fright" by "stress" in your question) is a physiological reaction, meaning that this reaction somehow helps the organism to overcome the stressful situation. From medical viewpoint the reaction to any external action can be:


physiological one (i.e. the one that is expected and is considered "good", helping the organism to adapt to this action).
pathophysiological:


as a side-effect of physiological reaction
as a result of nervous/humoral system overlast and depletion
as a reaction to unknown action
as a reaction to something mistaken for known action that is indeed something else



Mechanisms of tremor.

From mechanical viewpoint our body consists of dozens joints that are absolutely not fixed and have from two (moving in one plane) to three (for free movement in 3D, for example coxofemoral joint), thus giving our extremities an incredibly high number of degrees of freedom.

In order to sustain a certain posture our joints are equipped with antagonistic muscles: muscles that move the joint into opposite direction. The muscles, again, by design are very badly adapted for isotonic action. That basically means they cannot keep the same pressure for long time and the only way to get a fix posture for the whole body is to keep sending repetitive pulses to antagonistic muscles so that none of them actually wins.

Normally the impulses are very short and frequent. They also have to come synchronously and out-of-phase, meaning that whenever one muscles contracts its antagonist should dilate and vise versa, so that no muscle rupture takes place because of the simultaneous contraction of two opposite muscles. This synchrony accounts for very subtle trembling of the body, almost not seen by a naked eye in healthy humans. This trembling is also called physiological tremor to designate its being normal, e.g. physiological.

There are two ways how this trembling can increase so that it becomes visible and sensible:


Due to impaired synchronisation between the pulses sent to the antagonistic muscles. Since these pulses are generated in brainstem nervous centers, the impairment of those (in case of Parkinson's desease) or some inhibiting input into them (as in case of cerebellar deseases) leads to desync of these pulses, the frequency goes down whereas the amplitude might increase, making the trembling visible.
Due to attenuated cell sensitivity to the incoming impulses. This happens if the muscle cells start to overreact to the normal impulses and respond with prolonged contraction (followed by longer refractory period when they are unable to respond any impulse, thereby missing frequent pulses and reducing the effective frequency). These is mainly caused due to special metabolic changes within and in the vicinity of the muscle cells. 


The most common metabolic change within the cell is either the increased Calcium concentration within muscle cells, leading to much stronger contraction, or increased sensitivity for Calcium (via Ca and ryanodin receptors), that leads to much abrupter Calcium concentration rise in cells and results in the same.

The reason for Ca to increase within the cells might be the intake of some known Calcium liberators, like caffein, increased concentration of the humoral factors that use Ca as second messenger, like adrenaline, insuline, thyroid factors etc. Those, again, can be released during some stress conditions, during artificial or temporal low sugar level and other factors. 

Shivering as a reaction to stress.

The shivering, or in medical terms tremor might appear due to the following mechanisms:


Massive release of adrenaline during the stress: both directly via the adrenaline receptors and indirectly by causing temporal hyperglycemia via the metabolic adrenaline receptors. The action of adrenaline is also increased due to concomitant release of corticosteroids.
(muss less probable in case of fright, however might be common in many other cases) Overlast of the hypothalamic/amygdalic/brainstem structures responsible for stress reaction with probable weakening of deep nuclei controls over the posture and muscle contraction.


Conclusion.

So, as you see, the tremor is rather a pathophysiological reaction when it appears as response to stress, a side-effect manifestation due to acute temporal increase in adrenaline concentration in blood. Funny enough, but exactly this tremor is referenced to as "physiological tremor" in medical literature, because this type of tremor is not indicative for any CNS or endocrine disorder, that is very common for other types of tremor (postural, intentional etc.).