Yes you can but of course you will be testing a different hypothesis to when you compared personal history of stroke to no history of stroke.  If your question is: "is survival analysis appropriate when there are no censored data?", the answer is yes the survival analysis is appropriate but will basically yield the same result if you perform a Mann-Whitney U test on your two groups with time or age as your dependent.  As the convention when showing survival or time-to-event data is to plot the stepped or notched curve, you might as well perform the survival analysis (this is also what most readers will expect/be familiar with).  I hope this helps.

Yes you can but of course you will be testing a different hypothesis to when you compared personal history of stroke to no history of stroke.  If your question is: "is survival analysis appropriate when there are no censored data?", the answer is yes the survival analysis is appropriate but will basically yield the same result if you perform a Mann-Whitney U test on your two groups with time or age as your dependent.  As the convention when showing survival or time-to-event data is to plot the stepped or notched curve, you might as well perform the survival analysis (this is also what most readers will expect/be familiar with).  I hope this helps.

I concur with Hefin but would add that it looks like your effective sample is small, i.e. the minimum of the those with/without family history among the 100, so communicating the level of uncertainty in estimates will be important and help readers better interpret the test result, i.e. to what extent is a failure to find significant difference (if this happens) attributable to sample size.

I agree David, hopefully an appropriate power calculation to estimate required group size has been performed before the study started ;) If not, there is a wealth of information on performing group size calculations for different statistical models, including survival models. These can be performed in programs like R and GPower (although I don't think the latter supports survival analysis). One point to note however, SPSS provides a post-hoc power analysis feature for many of its modelling procedures;    but you should err on the side of caution when interpreting these post-hoc power analyses, because the effect size used by these calculations is the effect size of the data and NOT of the minimum effect size you should specify as interesting prior to the study beginning. The result of this is that basically if your result is significant, the post-hoc power anaylsis will generally tell you the data was sufficiently powered, but if it isn't significant, the post-hoc power analysis will generally tell you that it wasn't sufficiently powered. Just something to bare in mind :)

Thank you gentlemen for your opinions above. I greatly appreciate that. I wanted to compare the survival % among those with stroke and had a family history of stroke as opposed to those who dont have a family history of stroke. I had the impression that, we can only use the kaplan meier curves when there are presence of censored observations. Obviously i was incorrect.   And yes power calculation has been performed - so it has all been taken care of. thanks again.

I was not so focused on power calculation in my earlier comment since that pertains to an earlier stage of the process. What I look for in analysis reports is the confidence intervals for the estimates since they convey both the estimate and the degree of uncertainty in the estimate. P-values for tests are also useful, especially when asking if there is evidence that two estimates are different, but as a biostat  reviewer, I raise a flag if the confidence intervals are not provided. Confidence intervals are often provided by the stats package procedure. In cases where they are not, they can always be determined using the bootstrap method.