In short, yes. The 1905 Revolution weakened tsarist autocracy on multiple levels and shook the Empire's political foundations to their very core. The outcomes of 1905 were all detrimental to the long-term viability of the Romanov state even though Nicholas II did retain his throne.
Although the monarchy survived the Revolution, it emerged very damaged by the events of 1905. Not only had the Revolution exposed the weaknesses of the Russian security apparatus to squelch revolution, the state's counter-attack was often bloody and ham-fisted. The counter-revolutionary Black Hundreds, a paramilitary ultranationalist group with loose connections to the Interior Ministry, did restore semblance of order, but in the process killed political opponents and their actions against national minorities like Jews was often indistinguishable from earlier pogroms. This not only damaged Nicholas II's international credibility, but the Black Hundreds galvanized a good deal of left-wing and radical opposition to the state. Although Eisenstein's montage of the massacre of Odessa lay twenty years in the future, the mixture of brutality and clumsiness underscored to many in the Empire's left that the state could not be compromised, but also that it was incompetent. Additionally, many of the liberal centrists such as the Kadets resented the Black Hundreds and the use of arbitrary state power.
The post-1905 political order restored some stability to the tsarist system, but this stability was tenuous at best. The new Duma possessed some powers of oversight, but it had little direct power over the tsar and his policies. Stephen Kotkin terms the post-1905 Duma system as "constitutional autocracy," and this moniker aptly fits the paradoxical nature of the postrevolutionary Empire. While tsarist power nominally reigned supreme, it was to work in conjunction with a parliamentary body elected on a highly restrictive franchise. Thus the Duma system pleased no one. Those Russian liberals in favor of the working with the monarchy soon became disillusioned with the inability of the state to compromise or cede more authority, while for his part, Nicholas II was ill-inclined to work with the system lest he lose more authority. While Nicholas II possessed an able chief minister in the form of Stolypin, the latter's association with the bloody suppression of the Revolution and his Bismarckian attitude towards elected bodies poisoned his relationship with Russia's liberals. Adding to Stolypin's problems was that Nicholas II himself did not like his minister, so Stolypin was in an even more precarious position when he could not achieve results.
Stolypin's fall was associated with his failure to get the Duma to approve of the extension of the Zemstva (a form of local government) to the largely Polish Western provinces. This highlights another problem of the Empire 1905 uncovered: ethnic fissures. While the Russian Empire was a great power, it was a heterogeneous one. The best estimates peg the Great Russian population at about 40%-45% of the empire's total population. Not only did this mean that appeals to Russian nationalism could not strengthen the tsar in an age of mass politics, but that the reflexive and often hostile attitude of the imperial state to national minorities poisoned this relationship, especially groups the state authorities perceived as innately disloyal such as Poles or Jews. The events of 1905 in the Western Provinces often had strong nationalist overtones, with Polish and Jewish labor groups arguing that settling the question of a just socioeconmic order was intertwined with national justice. Although the state managed to restore order, 1905 heightened the imperial state's paranoia about disloyal groups such as the Baltic Germans. This paranoia bore fruit during the First World War as it provided rationalization for mass displacements, pogroms, and ethnic cleansing. But while 1905 added further bile to the relationship between the Empire and its non-Russian subjects, the state's relationship with Great Russian nationalists was not exactly healthy either. As an imperial ruler of multiple ethnicities, the Romanovs could never fully sanction a Great Russian nationalist program and Russian national activists often felt let down by Nicholas II. The extreme violence meted out by groups like the Black Hundreds often went against Saint Petersburg's wishes and the modes of Russian nationalist politics was often at odds with imperial prerogatives.
Finally, many Bolsheviks in 1917 would argue that 1905 was a dress-rehearsal for 1917. While Lenin and company certainly did over-emphasize their role in 1905 and side-stepped the heterogeneity of the revolutionaries, this connection was not just a legitimizing fiction. Many of the actors of the 1917 Revolutions went into them determined not to make the same mistakes as in 1905. Kadets, for example, were determined to make the Duma more than an empty political chamber after the February Revolution and recognized that the Romanovs were as liability to make such an event happen. The one imperial institution that really could not capitalize on the 1905 experience was autocracy. The price of success in 1905 created too many enemies across the Russian political spectrum for Nicholas II to enjoy a degree of support. The Emperor's prestige had suffered from the death of a thousand cuts in the post-1905 period and the war was a capstone to his political failures. Stolypin and other Romanov ministers bought Nicholas II time, but this was an asset that proved to be quite fleeting.
For an introduction to 1905, Abraham Ascher's short book on the Revolution is a must for understanding this period. Theodore Weeks's textbook Across the Revolutionary Divide is another good introduction to the wider issues and problems that contextualize the events of 1905 and makes a good case as to why the Romanovs were living on borrowed time after this Revolution.