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Can SN1 reactions occur in compounds where the carbocation, even though is is initially $1^\circ$, can rearrange to form a more stable carbocation?

Examples cases:

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    $\begingroup$ Under typical lab conditions a primary carbocation is not likely to form unless there is stabilization by an adjacent double bond or benzene ring, or unless there is a neighboring group that can provide neighboring group stabilization - but then we really don't have a simple primary carbocation in such cases. BTW, in your first example, a H shift would produce an antiaromatic (4n electrons) cyclopentadienyl cation, so this won't occur. $\endgroup$ – ron Sep 18 '16 at 15:01
  • $\begingroup$ Well, a benzyl cation is technically a primary one, so … $\endgroup$ – Jan Sep 19 '16 at 13:03
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    $\begingroup$ Fairly sure neopentyl iodide reacts with aqueous Ag+ to give the rearranged product t-amyl alcohol $\endgroup$ – orthocresol♦ Sep 20 '16 at 17:16
  • $\begingroup$ @ron Do you mind posting an answer? Thanks! $\endgroup$ – Gaurang Tandon Mar 28 '18 at 13:15
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Your thinking is correct that they can rearrange and then form stable carbocation (though your first example is wrong as it would become anti-aromatic after rearrangement) , but the answer to your question is NO , they would be substituted by SN2 mechanism being 1 degree . The reason behind this is that the compound will not try to form a carbocation first where it is not that stable , you can think of it in this way that at the initial stage the compound doesn't know that it can rearrange later to form stable carbocation, this is something that we can see but not the compound and thus it will go by normal SN2 mechanism.

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